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Journal articles on the topic 'Limiting absorption principle'

Author: Grafiati

Published: 1 June 2024

Last updated: 31 July 2025

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1

Renger, Walter. "Limiting Absorption Principle for Singularly Perturbed Operators." Mathematische Nachrichten 228, no. 1 (2001): 163–87. http://dx.doi.org/10.1002/1522-2616(200108)228:1<163::aid-mana163>3.0.co;2-v.

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2

Royer, Julien. "Limiting Absorption Principle for the Dissipative Helmholtz Equation." Communications in Partial Differential Equations 35, no. 8 (2010): 1458–89. http://dx.doi.org/10.1080/03605302.2010.490287.

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3

Datchev, Kiril. "Quantitative Limiting Absorption Principle in the Semiclassical Limit." Geometric and Functional Analysis 24, no. 3 (2014): 740–47. http://dx.doi.org/10.1007/s00039-014-0273-8.

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4

Ben-Artzi, Matania, and Allen Devinatz. "The limiting absorption principle for partial differential operators." Memoirs of the American Mathematical Society 66, no. 364 (1987): 0. http://dx.doi.org/10.1090/memo/0364.

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5

Itakura, Kyohei. "Limiting Absorption Principle and Radiation Condition for Repulsive Hamiltonians." Funkcialaj Ekvacioj 64, no. 2 (2021): 199–223. http://dx.doi.org/10.1619/fesi.64.199.

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6

de Monvel, Anne Boutet, and Radu Purice. "Limiting absorption principle for schrödinger hamiltonians with magnetic fields." Communications in Partial Differential Equations 19, no. 1-2 (1994): 89–117. http://dx.doi.org/10.1080/03605309408821010.

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7

Kopylova, E. "Limiting absorption principle for the 1D discrete Dirac equation." Russian Journal of Mathematical Physics 22, no. 1 (2015): 34–38. http://dx.doi.org/10.1134/s1061920815010069.

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8

Balslev, E., and B. Helffer. "Limiting absorption principle and resonances for the Dirac operator." Advances in Applied Mathematics 13, no. 2 (1992): 186–215. http://dx.doi.org/10.1016/0196-8858(92)90009-l.

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9

Taira, Kouichi. "Limiting absorption principle on Lp-spaces and scattering theory." Journal of Mathematical Physics 61, no. 9 (2020): 092106. http://dx.doi.org/10.1063/5.0011805.

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10

Jecko, Thierry, and Aiman Mbarek. "Limiting Absorption Principle for Schrödinger Operators with Oscillating Potentials." Documenta Mathematica 22 (2017): 727–76. http://dx.doi.org/10.4171/dm/577.

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11

Levendorski\u{\i}, S. Z. "Acoustic waves in perturbed periodic layer: a limiting absorption principle." Asymptotic Analysis 16, no. 1 (1998): 15–24. https://doi.org/10.3233/asy-1998-260.

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The acoustic wave propagator in a perturbed periodic layer $0< z< 1$ is given by [Formula: see text] where the speed of sound $c$ and density $\rho$ are short‐range perturbations of functions periodic in $(x, y)$ . A ‘limiting absorption principle’ for $H$ is established between suitably weighted $L_{2}$ ‐spaces. The limiting values of the resolvent are shown to be Hölder continuous at generic points of the real axis.

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12

Hoang, Vu. "The Limiting Absorption Principle for a Periodic Semi-Infinite Waveguide." SIAM Journal on Applied Mathematics 71, no. 3 (2011): 791–810. http://dx.doi.org/10.1137/100791798.

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13

Bonnet-Bendhia, Anne-Sophie, and Axel Tillequin. "A limiting absorption principle for scattering problems with unbounded obstacles." Mathematical Methods in the Applied Sciences 24, no. 14 (2001): 1089–111. http://dx.doi.org/10.1002/mma.259.

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14

Carey, Alan, Fritz Gesztesy, Jens Kaad, et al. "On the Global Limiting Absorption Principle for Massless Dirac Operators." Annales Henri Poincaré 19, no. 7 (2018): 1993–2019. http://dx.doi.org/10.1007/s00023-018-0675-5.

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15

ZHANG, BO. "On the limiting absorption and amplitude principles for transmission problems with unbounded interfaces." Mathematical Proceedings of the Cambridge Philosophical Society 122, no. 2 (1997): 343–56. http://dx.doi.org/10.1017/s0305004197001874.

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We consider the transmission problem for second-order differential equations with unbounded interfaces. The spaces B and B* are used to prove the limiting absorption principle for the steady-state problem and to establish the resolvent estimate at low frequencies for the steady-state operator. These are then applied in showing the validity of the limiting amplitude principle for such an operator.

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16

Cacciafesta, Federico, Piero D'Ancona, and Renato Lucà. "A limiting absorption principle for the Helmholtz equation with variable coefficients." Journal of Spectral Theory 8, no. 4 (2018): 1349–92. http://dx.doi.org/10.4171/jst/229.

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17

Boussaid, Nabile, and Andrew Comech. "Limiting absorption principle and virtual levels of operators in Banach spaces." Annales mathématiques du Québec 46, no. 1 (2021): 161–80. http://dx.doi.org/10.1007/s40316-021-00181-7.

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18

SHIMIZU, Shoji. "Limiting absorption principle for the second quantization of self-adjoint operators." Hokkaido Mathematical Journal 39, no. 2 (2010): 239–59. http://dx.doi.org/10.14492/hokmj/1277385663.

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19

Vainberg, B., and Marc Durand. "Limiting Absorption Principle for Stratified Operators with Thresholds: A General Method." Applicable Analysis 82, no. 8 (2003): 821–38. http://dx.doi.org/10.1080/0003681031000154945.

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20

Mandich, Marc-Adrien. "The limiting absorption principle for the discrete Wigner–von Neumann operator." Journal of Functional Analysis 272, no. 6 (2017): 2235–72. http://dx.doi.org/10.1016/j.jfa.2016.09.022.

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21

Zubeldia, Miren. "Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 144, no. 4 (2014): 857–90. http://dx.doi.org/10.1017/s0308210512000996.

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We study the Helmholtz equationin ℝd with magnetic and electric potentials that are singular at the origin and decay at ∞. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.

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22

Mokeeva, N. V. "The limiting absorption principle in the problem of a transparent wedge." Journal of Mathematical Sciences 142, no. 6 (2007): 2597–604. http://dx.doi.org/10.1007/s10958-007-0147-9.

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23

Gérard, Christian. "A proof of the abstract limiting absorption principle by energy estimates." Journal of Functional Analysis 254, no. 11 (2008): 2707–24. http://dx.doi.org/10.1016/j.jfa.2008.02.015.

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24

Zhang, Bo. "Radiation condition and limiting amplitude principle for acoustic propagators with two unbounded media." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 128, no. 1 (1998): 173–92. http://dx.doi.org/10.1017/s0308210500027220.

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Consider the diffraction problem for perturbed acoustic propagators with perturbations decreasing slowly at infinity. The propagation speed is discontinuous at the interface of two unbounded media, and the interface may be an arbitrary and smooth surface locally. A Sommerfeld radiation condition is introduced for the acoustic propagator, and is then used to establish the limiting absorption principle and the resolvent estimate at low frequencies for such an operator. Furthermore, we prove the existence of a unique solution to the diffraction problem and the validity of the limiting amplitude p

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25

EIDUS, D. "WAVE FRONTS AND THE RADIATION PRINCIPLE." Reviews in Mathematical Physics 19, no. 08 (2007): 805–21. http://dx.doi.org/10.1142/s0129055x07003115.

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We are concerned with the construction of Sommerfeld-type radiation conditions for stationary acoustic oscillations in inhomogeneous media with densities independent of r. It is shown that such radiation conditions exist iff there exists a one-parameter family of closed homothetic star-shaped (with respect to origin) wave fronts. These radiation conditions select the same solutions of the reduced wave equation as the limiting absorption principle.

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26

Popoff, Nicolas, and Eric Soccorsi. "Limiting absorption principle for the magnetic Dirichlet Laplacian in a half-plane." Communications in Partial Differential Equations 41, no. 6 (2016): 879–93. http://dx.doi.org/10.1080/03605302.2016.1167081.

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27

Nosich, A. I. "Radiation conditions, limiting absorption principle, and general relations in open waveguide scattering." Journal of Electromagnetic Waves and Applications 8, no. 3 (1994): 329–53. http://dx.doi.org/10.1163/156939394x00902.

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28

Nakamura, Gen, and Jenn-Nan Wang. "The limiting absorption principle for the two-dimensional inhomogeneous anisotropic elasticity system." Transactions of the American Mathematical Society 358, no. 1 (2004): 147–65. http://dx.doi.org/10.1090/s0002-9947-04-03609-8.

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29

DE MONVEL-BERTHIER, ANNE BOUTET, VLADIMIR GEORGESCU, and MARIUS MANTOIU. "LOCALLY SMOOTH OPERATORS AND THE LIMITING ABSORPTION PRINCIPLE FOR N-BODY HAMILTONIANS." Reviews in Mathematical Physics 05, no. 01 (1993): 105–89. http://dx.doi.org/10.1142/s0129055x93000048.

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We develop a variant of the (abstract) Mourre theory under very weak assumptions of regularity on the hamiltonian H with respect to the conjugate operator A. We find large classes of H-smooth operators and prove the limiting absorption principle in a class of (abstract) Besov spaces. As an example we extend the results of Agmon and Hörmander from the two-body to the N-body case.

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30

Martin, Alexandre. "On the Limiting absorption principle for a new class of Schrödinger Hamiltonians." Confluentes Mathematici 10, no. 1 (2018): 63–94. http://dx.doi.org/10.5802/cml.46.

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31

Kadowaki, Mitsuteru. "The limiting absorption principle for the acoustic wave operators in two unbounded media." Tsukuba Journal of Mathematics 17, no. 2 (1993): 345–62. http://dx.doi.org/10.21099/tkbjm/1496162267.

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32

Kumura, Hironori. "Limiting absorption principle on manifolds having ends with various measure growth rate limits." Proceedings of the London Mathematical Society 107, no. 3 (2013): 517–48. http://dx.doi.org/10.1112/plms/pds057.

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33

Behrndt, Jussi, Markus Holzmann, Andrea Mantile та Andrea Posilicano. "Limiting absorption principle and scattering matrix for Dirac operators with δ-shell interactions". Journal of Mathematical Physics 61, № 3 (2020): 033504. http://dx.doi.org/10.1063/1.5123289.

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34

Melgaard, Michael. "Optimal limiting absorption principle for a Schrödinger type operator on a Lipschitz cylinder." manuscripta mathematica 118, no. 2 (2005): 253–70. http://dx.doi.org/10.1007/s00229-005-0591-0.

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35

DeBièvre, S., and D. W. Pravica. "Spectral analysis for optical fibres and stratified fluids I: The limiting absorption principle." Journal of Functional Analysis 98, no. 2 (1991): 404–36. http://dx.doi.org/10.1016/0022-1236(91)90085-j.

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36

Nguyen, Hoai-Minh. "Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients." Journal de Mathématiques Pures et Appliquées 106, no. 2 (2016): 342–74. http://dx.doi.org/10.1016/j.matpur.2016.02.013.

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37

Boussaid, Nabile, and Sylvain Golénia. "Limiting Absorption Principle for Some Long Range Perturbations of Dirac Systems at Threshold Energies." Communications in Mathematical Physics 299, no. 3 (2010): 677–708. http://dx.doi.org/10.1007/s00220-010-1099-3.

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38

Burak Erdoğan, M., Michael Goldberg, and William R. Green. "Limiting Absorption Principle and Strichartz Estimates for Dirac Operators in Two and Higher Dimensions." Communications in Mathematical Physics 367, no. 1 (2018): 241–63. http://dx.doi.org/10.1007/s00220-018-3231-8.

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39

Mandel, Rainer. "The Limiting Absorption Principle for Periodic Differential Operators and Applications to Nonlinear Helmholtz Equations." Communications in Mathematical Physics 368, no. 2 (2019): 799–842. http://dx.doi.org/10.1007/s00220-019-03363-1.

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40

Devinatz, Allen, Richard Moeckel, and Peter Rejto. "A limiting absorption principle for Schr�dinger operators with Von Neumann-Wigner type potentials." Integral Equations and Operator Theory 14, no. 1 (1991): 13–68. http://dx.doi.org/10.1007/bf01194926.

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41

Shimizu, Senjo. "The Limiting Absorption Principle for Elastic Wave Propagation Problems in Perturbed Stratified Media ℝ3". Mathematical Methods in the Applied Sciences 19, № 3 (1996): 187–215. http://dx.doi.org/10.1002/(sici)1099-1476(199602)19:3<187::aid-mma766>3.0.co;2-m.

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42

FRÖHLICH, JÜRG, MARCEL GRIESEMER, and ISRAEL MICHAEL SIGAL. "SPECTRAL RENORMALIZATION GROUP AND LOCAL DECAY IN THE STANDARD MODEL OF NON-RELATIVISTIC QUANTUM ELECTRODYNAMICS." Reviews in Mathematical Physics 23, no. 02 (2011): 179–209. http://dx.doi.org/10.1142/s0129055x11004266.

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We prove a limiting absorption principle for the standard model of non-relativistic quantum electrodynamics (QED) and for Nelson's model describing interactions of electrons with phonons. To this end, we use the spectral renormalization group technique on the continuous spectrum in conjunction with Mourre theory.

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43

DE MONVEL, ANNE BOUTET, and JAOUAD SAHBANI. "ON THE SPECTRAL PROPERTIES OF DISCRETE SCHRÖDINGER OPERATORS." Reviews in Mathematical Physics 11, no. 09 (1999): 1061–78. http://dx.doi.org/10.1142/s0129055x99000337.

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We use the method of the conjugate operator to prove the limiting absorption principle and the absence of the singular continuous spectrum for the discrete Schrödinger operator. We also obtain local decay estimates. Our results apply to a large class of perturbating potentials V tending arbitrarily slowly to zero at infinity.

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44

NAKAZAWA, Hideo. "The Principle of Limiting Absorption for the Non-Selfadjoint Schrödinger Operator with Energy Dependent Potential." Tokyo Journal of Mathematics 23, no. 2 (2000): 519–36. http://dx.doi.org/10.3836/tjm/1255958686.

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45

Kalvin, Victor. "Limiting Absorption Principle and Perfectly Matched Layer Method for Dirichlet Laplacians in Quasi-cylindrical Domains." SIAM Journal on Mathematical Analysis 44, no. 1 (2012): 355–82. http://dx.doi.org/10.1137/110834287.

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46

Perfekt, Karl-Mikael. "Plasmonic eigenvalue problem for corners: Limiting absorption principle and absolute continuity in the essential spectrum." Journal de Mathématiques Pures et Appliquées 145 (January 2021): 130–62. http://dx.doi.org/10.1016/j.matpur.2020.07.001.

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47

Eidus, D. "The limiting absorption principle for an acoustic equation with a refraction coefficient vanishing at infinity." Asymptotic Analysis 63, no. 3 (2009): 143–50. http://dx.doi.org/10.3233/asy-2009-0936.

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48

Murata, Minoru, and Tetsuo Tsuchida. "Asymptotics of Green functions and the limiting absorption principle for elliptic operators with periodic coefficients." Journal of Mathematics of Kyoto University 46, no. 4 (2006): 713–54. http://dx.doi.org/10.1215/kjm/1250281601.

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49

Kirsch, Andreas, and Armin Lechleiter. "The Limiting Absorption Principle and a Radiation Condition for the Scattering by a Periodic Layer." SIAM Journal on Mathematical Analysis 50, no. 3 (2018): 2536–65. http://dx.doi.org/10.1137/17m1118920.

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50

Mandel, Rainer. "Uncountably Many Solutions for Nonlinear Helmholtz and Curl-Curl Equations." Advanced Nonlinear Studies 19, no. 3 (2019): 569–93. http://dx.doi.org/10.1515/ans-2019-2050.

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Abstract We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. The constructed solutions are mildly localized as they lie in the essential spectrum of the corresponding linear operator. As a new auxiliary tool a limiting absorption principle for the curl-curl operator is proved.

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