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Journal articles on the topic 'Green's functions'

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Published: 4 June 2021

Last updated: 15 June 2025

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1

Ignatchenko, Valter A., and Denis S. Tsikalov. "Green’s Functions of Spin and Electromagnetic Waves in the Sinusoidal Superlattice." Solid State Phenomena 233-234 (July 2015): 47–50. http://dx.doi.org/10.4028/www.scientific.net/ssp.233-234.47.

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The problem of finding the Green's function of spin and electromagnetic waves in the sinusoidal superlattice is considered. An analytical expression for the spectral representation of the Green's function has been found in the form of ascending continued fractions, the particular denominators of which are ordinary continued fractions. The Green’s function in the-space has been found by the numerical Fourier transformation of the Greens’s function found in the spectral representation.

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2

Rabello, S. J., L. C. de Albuquerque, and A. N. Vaidya. "Grassmann Green's functions." Journal of Physics A: Mathematical and General 27, no. 19 (1994): 6571–77. http://dx.doi.org/10.1088/0305-4470/27/19/027.

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3

Chung, Fan, and S. T. Yau. "Discrete Green's Functions." Journal of Combinatorial Theory, Series A 91, no. 1-2 (2000): 191–214. http://dx.doi.org/10.1006/jcta.2000.3094.

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4

KIGAMI, JUN, DANIEL R. SHELDON, and ROBERT S. STRICHARTZ. "GREEN'S FUNCTIONS ON FRACTALS." Fractals 08, no. 04 (2000): 385–402. http://dx.doi.org/10.1142/s0218348x00000421.

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For a regular harmonic structure on a post-critically finite (p.c.f.) self-similar fractal, the Dirichlet problem for the Laplacian can be solved by integrating against an explicitly given Green's function. We give a recursive formula for computing the values of the Green's function near the diagonal, and use it to give sharp estimates for the decay of the Green's function near the boundary. We present data from computer experiments searching for the absolute maximum of the Green's function for two different examples, and we formulate two radically different conjectures for where the maximum occurs. We also investigate a local Green's function that can be used to solve an initial value problem for the Laplacian, giving an explicit formula for the case of the Sierpinski gasket. The local Green's function turns out to be unbounded, and in fact not even integrable, but because of cancelation, it is still possible to form a singular integral to solve the initial value problem if the given function satisfies a Hölder condition.

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5

Ramm, A. G., and Lige Li. "Estimates for Green's Functions." Proceedings of the American Mathematical Society 103, no. 3 (1988): 875. http://dx.doi.org/10.2307/2046868.

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6

Merriam, J. B. "Transverse stress: Green's functions." Journal of Geophysical Research 91, B14 (1986): 13903. http://dx.doi.org/10.1029/jb091ib14p13903.

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7

Beals, Richard, Bernard Gaveau, and Peter Greiner. "Uniforms hypoelliptic Green's functions." Journal de Mathématiques Pures et Appliquées 77, no. 3 (1998): 209–48. http://dx.doi.org/10.1016/s0021-7824(98)80069-x.

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8

Kochubei, A. N. "Onp-adic Green's functions." Theoretical and Mathematical Physics 96, no. 1 (1993): 854–65. http://dx.doi.org/10.1007/bf01074114.

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9

Stefanucci, Gianluca, Andrea Marini, and Stefano Bellucci. "Non‐Equilibrium Green's Functions." physica status solidi (b) 256, no. 7 (2019): 1900335. http://dx.doi.org/10.1002/pssb.201900335.

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10

Granath, M., A. Sabashvili, H. U. R. Strand, and S. Östlund. "Discretized thermal Green's functions." Annalen der Physik 524, no. 3-4 (2012): 147–52. http://dx.doi.org/10.1002/andp.201100262.

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11

Li, Peter, and Luen-Fai Tam. "Green's functions, harmonic functions, and volume comparison." Journal of Differential Geometry 41, no. 2 (1995): 277–318. http://dx.doi.org/10.4310/jdg/1214456219.

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12

Kim, Daehwan, Donghyeon Kim, Gihoon Byun, J. S. Kim, and Heechun Song. "Enhancement of Green's functions based on striation pattern." Journal of the Acoustical Society of America 154, no. 4_supplement (2023): A356. http://dx.doi.org/10.1121/10.0023787.

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Enhancement of Green's function is accomplished from the striation pattern obtained from data. The waveguide invariant theory allows a Green's function observed at one location to be extrapolated into adjacent ranges [Song and Byun, J. Acoust. Soc. Am. 147, 2150–2158 (2020)]. Conversely, Green's functions observed at adjacent ranges can converge towards a central location for coherent combination to improve the signal-to-noise ratio (SNR). This can be accomplished from the frequency shift in the striation pattern without prior range information of each Green's functions. We demonstrate a significant improvement of SNR in the broadband Green's function from a moving ship in shallow water.

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13

Cho, Manki. "Steklov approximations of Green’s functions for Laplace equations." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 39, no. 4 (2020): 991–1003. http://dx.doi.org/10.1108/compel-09-2019-0357.

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Purpose This paper aims to present a meshless technique to find the Green’s functions for solutions of Laplacian boundary value problems on rectangular domains. This paper also investigates a theoretical basis for the Steklov series expansion methods to reduce and estimate the error of numerical approaches for the boundary correction kernel of the Laplace operator. Design/methodology/approach The main interest is how the Green's functions differ from the fundamental solution of the Laplace operator. Steklov expansion methods for finding the correction term are supported by the analysis that bases of the class of all finite harmonic functions can be formed using harmonic Steklov eigenfunctions. These functions construct a basis of the space of solutions of harmonic boundary value problems and their boundary traces generate an orthogonal basis of the trace space of solutions on the boundary. Findings The main conclusion is that the boundary correction term for the Green's functions is well-approximated by Steklov expansions with a few Steklov eigenfunctions. The error estimates for the Steklov approximations of the boundary correction term involved in Dirichlet or Robin boundary value problems are found. They appear to provide very good approximations in the interior of the region and become quite oscillatory close to the boundary. Originality/value This paper concentrates to document the first attempt to find the Green's function for various harmonic boundary value problems with the explicit Steklov eigenfunctions without concerns regarding discretizations when the region is a rectangle.

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14

Song, Xi J., and Donald V. Helmberger. "Pseudo green's functions and waveform tomography." Bulletin of the Seismological Society of America 88, no. 1 (1998): 304–12. http://dx.doi.org/10.1785/bssa0880010304.

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Abstract Retrieving source characteristics for moderate-sized earthquakes in sparsely instrumented regions has been made possible in recent years, through the modeling of waveforms at regional distances. The techniques used in such studies model waveforms successfully at long period, using Green's functions for simple 1D crustal models. For small earthquakes (M &lt; 4), however, long-period signals are usually noisy, and modeling short-period waveforms requires refined Green's functions such as used in the empirical Green's function (eGf) approach. In this article, we present a new technique that generates such Green's functions by perturbing individual generalized ray responses calculated from a 1D model. The model is divided into blocks, and velocities in the blocks are allowed to vary, which shifts the arrival time of the individual rays similar to conventional tomography. The amplitudes of the rays are perturbed independently to accommodate local velocity variations in the structure. For moderate-sized earthquakes with known source mechanism and time history, the velocity variation in each block and the amplification factor for individual rays can be optimized using a simulated annealing algorithm. The resulting modified Green's functions, pseudo Green's functions (pGfs), can be used to study the relative location and characteristics of neighboring events. The method is also useful in retrieving 2D structure, which is essentially waveform tomography.

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15

Beylkin, Gregory, Christopher Kurcz, and Lucas Monzón. "Fast algorithms for Helmholtz Green's functions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2100 (2008): 3301–26. http://dx.doi.org/10.1098/rspa.2008.0161.

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The formal representation of the quasi-periodic Helmholtz Green's function obtained by the method of images is only conditionally convergent and, thus, requires an appropriate summation convention for its evaluation. Instead of using this formal sum, we derive a candidate Green's function as a sum of two rapidly convergent series, one to be applied in the spatial domain and the other in the Fourier domain (as in Ewald's method). We prove that this representation of Green's function satisfies the Helmholtz equation with the quasi-periodic condition and, furthermore, leads to a fast algorithm for its application as an operator. We approximate the spatial series by a short sum of separable functions given by Gaussians in each variable. For the series in the Fourier domain, we exploit the exponential decay of its terms to truncate it. We use fast and accurate algorithms for convolving functions with this approximation of the quasi-periodic Green's function. The resulting method yields a fast solver for the Helmholtz equation with the quasi-periodic boundary condition. The algorithm is adaptive in the spatial domain and its performance does not significantly deteriorate when Green's function is applied to discontinuous functions or potentials with singularities. We also construct Helmholtz Green's functions with Dirichlet, Neumann or mixed boundary conditions on simple domains and use a modification of the fast algorithm for the quasi-periodic Green's function to apply them. The complexity, in dimension d ≥2, of these algorithms is ( κ d log κ + C (log ϵ −1 ) d ), where ϵ is the desired accuracy, κ is proportional to the number of wavelengths contained in the computational domain and C is a constant. We illustrate our approach with examples.

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16

Hisada, Yoshiaki. "An efficient method for computing Green's functions for a layered half-space with sources and receivers at close depths." Bulletin of the Seismological Society of America 84, no. 5 (1994): 1456–72. http://dx.doi.org/10.1785/bssa0840051456.

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Abstract We propose an analytical method to compute efficiently the displacement and stress of static and dynamic Green's functions for viscoelastic layered half-spaces. When source and receiver depths are close, it is difficult to compute Green's functions of the layered half-space, because their integrands, whose variable of integration is the horizontal wavenumber, oscillate with only slowly decreasing amplitude. In particular, when the depths are equal, it is extremely difficult to compute the stress Green's functions, because their integrands oscillate with increasing amplitude. To remedy this problem, we first derive the asymptotic solutions, which converge to the integrands of Green's functions with increasing wavenumber. For this purpose, we modify the generalized R/T (reflection and transmission) coefficient method (Luco and Apsel; 1983) to be completely free from growing exponential terms, which are the obstacles to finding the asymptotic solutions. By subtracting the asymptotic solutions from the integrands of the corresponding Green's functions, we obtain integrands that converge rapidly to zero. We can, therefore, significantly reduce the range of wavenumber integration. Since the asymptotic solutions are expressed by the products of Bessel functions and simple exponential functions, they are analytically integrable. Finally, we obtain accurate Green's functions by adding together numerical and analytical integrations. We first show this asymptotic technique for Green's functions due to point sources, and extend it to Green's functions due to dipole sources. Finally, we demonstrate the validity and efficiency of our method for various cases.

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17

Rambousky, R., S. Tkachenko, and J. Nitsch. "A novel solution algorithm for nonlinearly loaded transmission lines inside resonating enclosures." Advances in Radio Science 12 (November 10, 2014): 135–42. http://dx.doi.org/10.5194/ars-12-135-2014.

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Abstract. Nonlinearly loaded lossless transmission lines inside a rectangular cavity are studied using the left- and right-hand Green's functions of the problem in time domain. These Green's functions are developed for a transmission line with quasi-matched loads. This ensures Green's functions of a short duration. Therefore, the amount of frequency data necessary to obtain time-domain Green's functions is quite limited. The time-domain Green's functions are finally convolved with the left- and right-hand line voltages. With this technique it is possible to treat arbitrarily loaded transmission lines in resonators. An example is presented to demonstrate the applicability of this technique to a transmission line with a simple diode as nonlinear load.

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18

Delong, Steven, Florencio Balboa Usabiaga, Rafael Delgado-Buscalioni, Boyce E. Griffith, and Aleksandar Donev. "Brownian dynamics without Green's functions." Journal of Chemical Physics 140, no. 13 (2014): 134110. http://dx.doi.org/10.1063/1.4869866.

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19

Hanyga, Andrzej. "Time-Domain Poroelastic Green's Functions." Journal of Computational Acoustics 11, no. 03 (2003): 491–501. http://dx.doi.org/10.1142/s0218396x0300205x.

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A method previously developed for asymptotic solution of systems of integro-differential equations with singular memory is applied to the determination of the time-domain asymptotic Green's function of Biot's poroelasticity. Asymptotic time-domain Green's functions are constructed in a neighborhood of the wavefronts. The general anisotropic medium as well as the isotropic case are considered.

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20

Jorgenson, J., and J. Kramer. "Bounds on canonical Green's functions." Compositio Mathematica 142, no. 03 (2006): 679–700. http://dx.doi.org/10.1112/s0010437x06001990.

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21

Morfey, C. L., C. J. Powles, and M. C. M. Wright. "Green's Functions in Computational Aeroacoustics." International Journal of Aeroacoustics 10, no. 2-3 (2011): 117–59. http://dx.doi.org/10.1260/1475-472x.10.2-3.117.

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22

WEIGLHOFER, WERNER S. "Green's functions and magnetized ferrites." International Journal of Electronics 73, no. 4 (1992): 763–71. http://dx.doi.org/10.1080/00207219208925711.

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23

Padkj�r, S�ren Berg, and Esper Dalgaard. "Green's functions for separable potentials." Theoretica Chimica Acta 89, no. 5-6 (1994): 287–300. http://dx.doi.org/10.1007/bf01114102.

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24

Chasseigne, Emmanuel, and Raúl Ferreira. "Monotone approximations of Green's functions." Comptes Rendus Mathematique 339, no. 6 (2004): 395–400. http://dx.doi.org/10.1016/j.crma.2004.07.003.

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25

Gonis, A. "Green's functions for interstitial impurities." Physical Review B 34, no. 2 (1986): 1290–92. http://dx.doi.org/10.1103/physrevb.34.1290.

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26

Leung, K. W., Y. W. Liu, P. Yang, and K. K. Mei. "Maxwellian circuits and Green's functions." Microwave and Optical Technology Letters 41, no. 4 (2004): 318–20. http://dx.doi.org/10.1002/mop.20129.

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27

Herrera, William J., Herbert Vinck-Posada, and Shirley Gómez Páez. "Green's functions in quantum mechanics courses." American Journal of Physics 90, no. 10 (2022): 763–69. http://dx.doi.org/10.1119/5.0065733.

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The use of Green's functions is valuable when solving problems in electrodynamics, solid-state physics, and many-body physics. However, its role in quantum mechanics is often limited to the context of scattering by a central force. This work shows how Green's functions can be used in other examples in quantum mechanics courses. In particular, we introduce time-independent Green's functions and the Dyson equation to solve problems with an external potential. We calculate the reflection and transmission coefficients of scattering by a Dirac delta barrier and the energy levels and local density of states of the infinite square well potential.

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28

Özdemir, Özgür, Hazel Yücel, Yaǧmur Ece Uçar, Bariş Erbaş, and Nihal Ege. "Green's functions for a layered high-contrast acoustic media." Journal of the Acoustical Society of America 151, no. 6 (2022): 3676–84. http://dx.doi.org/10.1121/10.0011547.

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A parametric approach based on parametric analysis of the acoustical properties of a layered media is proposed to derive a reduced layered Green's function. The approach relies on the smallness of one of the problem parameters and allows a simpler form of Green's function by disregarding the smaller parametric terms. Several illustrative examples comparing the amplitudes of exact and reduced Green's function for small parameter of density ratio in various source and observation location setups are presented. It is demonstrated that the CPU times calculated at different points decrease considerably for the reduced Green's function, further justifying the presented method.

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29

Wu, Kuang-Chong. "Dynamic Green's Functions for Anisotropic Materials Under Anti-Plane Deformation." Journal of Mechanics 15, no. 1 (1999): 11–15. http://dx.doi.org/10.1017/s1727719100000277.

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ABSTRACTThe dynamic Green's function due to an impulse in an infinite anisotropic medium under anti-plane deformation is derived by the method of Smirnov [1] for two-dimensional wave equation. The Green's function is inversely proportional to the time t and an effective dynamic shear modulus. It is shown that the tractions on the planes passing through the source point vanish identically. Based on the free-space Green's function, the Green's functions for wedges, semi-infinite media and strips are obtained.

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30

BARTKOWIAK, M., P. MÜNGER, and K. A. CHAO. "HIGH-DENSITY EXPANSION FOR THE SPINLESS FERMION MODEL III: GREEN'S FUNCTIONS." International Journal of Modern Physics B 04, no. 13 (1990): 2025–40. http://dx.doi.org/10.1142/s0217979290001017.

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The single-particle electron Green's function and the charge-fluctuation Green's function for the spin-polarized fermion lattice gas are calculated within the framework of the high-density expansion up to the first order in 1/z. Violation of some conditions of consistency of diagrammatic perturbation expansion approximation schemes are discussed. Relations between the Green's functions and corresponding approximate free energy are established. Two kinds of approximations for Green's functions for the charge ordered phase are constructed and applied to determine the band structure of the spinless fermion model. The Green's functions for the nonordered phase are used to study the phase diagram of the model for finite temperatures and arbitrary band filling.

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31

Enting, I. G. "Green's functions and response functions in geochemical modelling." Pure and Applied Geophysics PAGEOPH 123, no. 2 (1985): 328–43. http://dx.doi.org/10.1007/bf00877027.

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32

Kamigaichi, Osamu, Norio Matsumoto, and Fuyuki Hirose. "Green's function at depth of borehole observation required for precise estimation of the effect of ocean tidal loading near coasts." Geophysical Journal International 227, no. 1 (2021): 275–86. http://dx.doi.org/10.1093/gji/ggab216.

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SUMMARY We calculated Green's functions of displacements and strains caused by a surface load in surface and subsurface observations. Green's functions of displacements and strains at depth became different from those at the surface for a range of angular distances less than 0.01–0.1°. These Green's functions closely agree with the corresponding Boussinesq approximations for tidal loading at angular distances of less than about 0.01–0.001°. We examined the difference between the ocean tidal loading effect estimated by Green's functions at the surface and the effect for subsurface observations, and found a non-negligible difference when the ratio of distance between the coast and observatory to the deployment depth is smaller than 20. We compared amplitudes and phase shifts of areal and shear strains in the M2 tidal constituent observed by borehole strainmeters at 11 observatories with the theoretical strains using the Green's functions at the deployment depth and those at the surface. The theoretical strains using Green's function at the deployment depth are much closer to the observed strains than theoretical strains at the surface at four observatories where the ratios of distance from the coast to the observatories to the deployment depth are small. These results suggest that Green's functions at the deployment depth are needed to estimate theoretical strains precisely near the coast.

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33

Rezaiee-Pajand, M., A. Aftabi Sani, and S. M. Hozhabrossadati. "Analyzing Free-Free Beams by Green's Functions and Fredholm Alternative Theorem." Journal of Mechanics 35, no. 1 (2017): 27–39. http://dx.doi.org/10.1017/jmech.2017.57.

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AbstractThis article deals with the analysis of free-free beams by an analytical method. The well-known Green's function method is employed, and exact solution for the problem is obtained. As a second problem, the simply supported-free beam with rotational rigid body motion is analyzed. It is initially shown that ordinary Green's functions cannot be constructed due to a mathematical contradiction. To remedy this limitation, the Fredholm Alternative Theorem is utilized. This theorem eliminates the contradiction and enables analysts to obtain modified Green's functions. The fundamental existence conditions are derived and thoroughly investigated from the structural point of view. Finally, the deflection functions of these beams are found using modified Green's functions.

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34

Hsu, Chia-Wen, and Chyanbin Hwu. "Green's functions for unsymmetric composite laminates with inclusions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2233 (2020): 20190437. http://dx.doi.org/10.1098/rspa.2019.0437.

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It is known that the stretching and bending deformations will be coupled together for the unsymmetric composite laminates under in-plane force and/or out-of-plane bending moment. Although Green's functions for unsymmetric composite laminates with elliptical elastic inclusions have been obtained by using Stroh-like formalism around 10 years ago, due to the ignoring of inconsistent rigid body movements of matrix and inclusion, the existing solution may lead to displacement discontinuity across the interface between matrix and inclusion. Due to the multi-valued characteristics of complex logarithmic functions appeared in Green's functions, special attention should be made on the proper selection of branch cuts of mapped variables. To solve these problems, in this study, the existing Green's functions are corrected and a simple way to correctly evaluate the mapped complex variable logarithmic functions is suggested. Moreover, to apply the obtained solutions to boundary element method, we also derive the explicit closed-form solution for Green's function of deflection. Since the continuity conditions along the interface have been satisfied in Green's functions, no meshes are required along the interface, which will save a lot of computational time and the results are much more accurate than any other numerical methods.

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35

TADEU, A., E. G. A. COSTA, J. ANTÓNIO, and P. AMADO-MENDES. "2.5D AND 3D GREEN'S FUNCTIONS FOR ACOUSTIC WEDGES: IMAGE SOURCE TECHNIQUE VERSUS A NORMAL MODE APPROACH." Journal of Computational Acoustics 21, no. 01 (2013): 1250025. http://dx.doi.org/10.1142/s0218396x12500257.

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2.5D and 3D Green's functions are implemented to simulate wave propagation in the vicinity of two-dimensional wedges. All Green's functions are defined by the image-source technique, which does not account directly for the acoustic penetration of the wedge surfaces. The performance of these Green's functions is compared with solutions based on a normal mode model, which are found not to converge easily for receivers whose distance to the apex is similar to the distance from the source to the apex. The applicability of the image source Green's functions is then demonstrated by means of computational examples for three-dimensional wave propagation. For this purpose, a boundary element formulation in the frequency domain is developed to simulate the wave field produced by a 3D point pressure source inside a two-dimensional fluid channel. The propagating domain may couple different dipping wedges and flat horizontal layers. The full discretization of the boundary surfaces of the channel is avoided since 2.5D Green's functions are used. The BEM is used to couple the different subdomains, discretizing only the vertical interfaces between them.

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36

Engliš, Miroslav, and Jaak Peetre. "Covariant differential operators and Green's functions." Annales Polonici Mathematici 66 (1997): 77–103. http://dx.doi.org/10.4064/ap-66-1-77-103.

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37

Li, Peter, and Luen-Fai Tam. "Symmetric Green's Functions on Complete Manifolds." American Journal of Mathematics 109, no. 6 (1987): 1129. http://dx.doi.org/10.2307/2374588.

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38

Süßmann, G., and H. D. Radecke. "Green's Functions in Robertson-Walker-Space." Zeitschrift für Naturforschung A 40, no. 1 (1985): 96–98. http://dx.doi.org/10.1515/zna-1985-0117.

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39

BAGHAI-WADJI, ALI R. "THEORY AND APPLICATIONS OF GREEN'S FUNCTIONS." International Journal of High Speed Electronics and Systems 10, no. 04 (2000): 949–1015. http://dx.doi.org/10.1142/s0129156400000696.

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In this chapter it is shown that three dimensional governing- and constitutive equations in transversally inhomogeous piezoelectric media can be diagonalized. A symbolic notation has been introduced which allows to perform the diagonalization simply by inspection. Diagonalized differential equations transform into eigenvalue forms in Fourier domain. Solving for the corresponding eigenpairs, the construction of various Green's functions has been demonstrated by several examples. In addition novel ideas for the calculation of self-actions in the boundary element method have been discussed. The work consists of four sections. Following a brief introduction in the first section, the diagonalization procedure is described in the second section. The presented methodology is a refinement of the author's ideas which were presented in various short courses. The third section on Green's function theory and the calculation of self-actions in the boundary element builds upon the author's lecture notes. The fourth section briefly summarizes our discussion and suggests directions for possible future research.

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40

Schweber, S. S. "The sources of Schwinger's Green's functions." Proceedings of the National Academy of Sciences 102, no. 22 (2005): 7783–88. http://dx.doi.org/10.1073/pnas.0405167101.

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41

Guttmann, Anthony J. "Lattice Green's functions in all dimensions." Journal of Physics A: Mathematical and Theoretical 43, no. 30 (2010): 305205. http://dx.doi.org/10.1088/1751-8113/43/30/305205.

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42

Shubin, M. A. "PSEUDODIFFERENCE OPERATORS AND THEIR GREEN'S FUNCTIONS." Mathematics of the USSR-Izvestiya 26, no. 3 (1986): 605–22. http://dx.doi.org/10.1070/im1986v026n03abeh001161.

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43

Klepfish, E. G., C. E. Creffield, and E. R. Pike. "Analytic continuation of Matsubara Green's functions." Nuclear Physics B - Proceedings Supplements 63, no. 1-3 (1998): 655–57. http://dx.doi.org/10.1016/s0920-5632(97)00862-1.

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44

Martin, P. A. "Multiple scattering and modified Green's functions." Journal of Mathematical Analysis and Applications 275, no. 2 (2002): 642–56. http://dx.doi.org/10.1016/s0022-247x(02)00318-9.

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45

Kerr, Arnold D., and Magdy A. El-Sibaie. "Green's functions for continuously supported plates." ZAMP Zeitschrift f�r angewandte Mathematik und Physik 40, no. 1 (1989): 15–38. http://dx.doi.org/10.1007/bf00945307.

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46

Duhamel, D. "Finite element computation of Green's functions." Engineering Analysis with Boundary Elements 31, no. 11 (2007): 919–30. http://dx.doi.org/10.1016/j.enganabound.2007.04.002.

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47

Tsamis, N. C., and R. P. Woodard. "Physical Green's functions in quantum gravity." Annals of Physics 215, no. 1 (1992): 96–155. http://dx.doi.org/10.1016/0003-4916(92)90301-2.

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48

Martinsson, Per-Gunnar, and Gregory J. Rodin. "Asymptotic expansions of lattice Green's functions." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 458, no. 2027 (2002): 2609–22. http://dx.doi.org/10.1098/rspa.2002.0985.

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Sanchez, Richard. "Duality, Green's functions and all that." Transport Theory and Statistical Physics 27, no. 5-7 (1998): 445–76. http://dx.doi.org/10.1080/00411459808205638.

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Culumovic, L., M. Leblanc, R. B. Mann, D. G. C. McKeon, and T. N. Sherry. "Operator regularization and multiloop Green's functions." Physical Review D 41, no. 2 (1990): 514–33. http://dx.doi.org/10.1103/physrevd.41.514.

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