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Journal articles on the topic 'Convolution Integral'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 February 2022

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1

PAP, ENDRE, and IVANA ŠTAJNER. "PSEUDO-CONVOLUTION BASED ON IDEMPOTENT OPERATION AS LIMIT OF g-CONVOLUTION." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 07, no. 06 (1999): 615–29. http://dx.doi.org/10.1142/s0218488599000520.

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Operation with functions known as pseudo-convolution and its generalization as well as theirs basic properties has been presented. Then, it has been proved that pseudo-convolution which core is pseudo-integral based on max or min decomposable measure can be obtained as limit of g-convolutions, i.e., pseudo-convolutions with pseudo-integrals based on ⊕-decomposable measures where ⊕ is generated pseudo-addition, as their cores.

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2

Korotkov, V. B. "Convolution Integral Operators." Siberian Mathematical Journal 59, no. 4 (2018): 677–80. http://dx.doi.org/10.1134/s0037446618040092.

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3

Pavlov, E. A. "Integral convolution operators." Mathematical Notes of the Academy of Sciences of the USSR 38, no. 1 (1985): 554–56. http://dx.doi.org/10.1007/bf01137467.

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4

Kılıçman, Adem. "On the Fresnel sine integral and the convolution." International Journal of Mathematics and Mathematical Sciences 2003, no. 37 (2003): 2327–33. http://dx.doi.org/10.1155/s0161171203211510.

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The Fresnel sine integralS(x), the Fresnel cosine integralC(x), and the associated functionsS+(x), S−(x), C+(x), andC−(x)are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel sine integral and its associated functions withx+r, xrare evaluated.

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5

Kiliçman, Adem, and Brian Fisher. "On the Fresnel integrals and the convolution." International Journal of Mathematics and Mathematical Sciences 2003, no. 41 (2003): 2635–43. http://dx.doi.org/10.1155/s0161171203211522.

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The Fresnel cosine integralC(x), the Fresnel sine integralS(x), and the associated functionsC+(x),C−(x),S+(x), andS−(x)are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions withx+randxrare evaluated.

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6

Zöckler, Malte, Detlev Stalling, and Hans-Christian Hege. "Parallel line integral convolution." Parallel Computing 23, no. 7 (1997): 975–89. http://dx.doi.org/10.1016/s0167-8191(97)00039-2.

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7

Peleshenko, B. I., and V. A. Katan. "On integral convolution operators." Mathematical Notes 66, no. 4 (1999): 451–54. http://dx.doi.org/10.1007/bf02679095.

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8

Al-Omari, Shrideh K. Q., and Dumitru Baleanu. "Convolution theorems associated with some integral operators and convolutions." Mathematical Methods in the Applied Sciences 42, no. 2 (2018): 541–52. http://dx.doi.org/10.1002/mma.5359.

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9

Margrave, Gary F. "Theory of nonstationary linear filtering in the Fourier domain with application to time‐variant filtering." GEOPHYSICS 63, no. 1 (1998): 244–59. http://dx.doi.org/10.1190/1.1444318.

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A general linear theory describes the extension of the convolutional method to nonstationary processes. This theory can apply any linear, nonstationary filter, with arbitrary time and frequency variation, in the time, Fourier, or mixed domains. The filter application equations and the expressions to move the filter between domains are all ordinary Fourier transforms or generalized convolutional integrals. Nonstationary transforms such as the wavelet transform are not required. There are many possible applications of this theory including: the one‐way propagation of waves through complex media,

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10

Selvaggi, Jerry P., and Jerry A. Selvaggi. "The Application of Real Convolution for Analytically Evaluating Fermi-Dirac-Type and Bose-Einstein-Type Integrals." Journal of Complex Analysis 2018 (May 6, 2018): 1–8. http://dx.doi.org/10.1155/2018/5941485.

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The Fermi-Dirac-type or Bose-Einstein-type integrals can be transformed into two convergent real-convolution integrals. The transformation simplifies the integration process and may ultimately produce a complete analytical solution without recourse to any mathematical approximations. The real-convolution integrals can either be directly integrated or be transformed into the Laplace Transform inversion integral in which case the full power of contour integration becomes available. Which method is employed is dependent upon the complexity of the real-convolution integral. A number of examples ar

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11

Al-Omari, Shrideh Khalaf. "A study on a class of modified Bessel-type integrals in a Fréchet space of Boehmians." Boletim da Sociedade Paranaense de Matemática 38, no. 4 (2019): 145–56. http://dx.doi.org/10.5269/bspm.v38i4.37463.

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In this paper, an attempt is being made to discuss a class of modified Bessel- type integrals on a set of generalized functions known as Boehmians. We show that the modified Bessel-type integral, with appropriately defined convolution products, obeys a fundamental convolution theorem which consequently justifis pursuing analysis in the Boehmian spaces. We describe two Fréchet spaces of Boehmians and extend the modifid Bessel-type integral between the diferent spaces. Furthermore, a convolution theorem and a class of basic properties of the extended integral such as linearity, continuity and co

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12

Giang, Bui Thi, and Nguyen Minh Tuan. "Generalized convolutions and the integral equations of the convolution type." Complex Variables and Elliptic Equations 55, no. 4 (2010): 331–45. http://dx.doi.org/10.1080/17476930902998886.

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13

Geum, Young Hee, Arjun Kumar Rathie, and Hwajoon Kim. "Matrix Expression of Convolution and Its Generalized Continuous Form." Symmetry 12, no. 11 (2020): 1791. http://dx.doi.org/10.3390/sym12111791.

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In this paper, we consider the matrix expression of convolution, and its generalized continuous form. The matrix expression of convolution is effectively applied in convolutional neural networks, and in this study, we correlate the concept of convolution in mathematics to that in convolutional neural network. Of course, convolution is a main process of deep learning, the learning method of deep neural networks, as a core technology. In addition to this, the generalized continuous form of convolution has been expressed as a new variant of Laplace-type transform that, encompasses almost all exis

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14

Duc, Dinh, and Nguyen Nhan. "Norm inequalities for new convolutions and their applications." Applicable Analysis and Discrete Mathematics 9, no. 1 (2015): 168–79. http://dx.doi.org/10.2298/aadm150109001d.

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Various Lp-weighted norm inequalities for some new types of convolutions are proved which generalize some known results on convolution norm inequalities. Applications are made in the field of integral transforms and differential equations.

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15

LE, T. A., and J. W. SANDER. "CONVOLUTIONS OF RAMANUJAN SUMS AND INTEGRAL CIRCULANT GRAPHS." International Journal of Number Theory 08, no. 07 (2012): 1777–88. http://dx.doi.org/10.1142/s1793042112501023.

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There exist several generalizations of the classical Dirichlet convolution, for instance the so-called A-convolutions analyzed by Narkiewicz. We shall connect the concept of A-convolutions satisfying a weak form of regularity and Ramanujan sums with the spectrum of integral circulant graphs. These generalized Cayley graphs, having circulant adjacency matrix and integral eigenvalues, comprise a great amount of arithmetical features. By use of our concept we obtain a multiplicative decomposition of the so-called energy of integral circulant graphs with multiplicative divisor sets. This will be f

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16

Yakubov, Askhab, and Lamara Shankishvili. "Some inequalites for convolution integral transforms." Integral Transforms and Special Functions 2, no. 1 (1994): 65–76. http://dx.doi.org/10.1080/10652469408819038.

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17

Zhanping Liu and R. J. Moorhead. "Accelerated unsteady flow line integral convolution." IEEE Transactions on Visualization and Computer Graphics 11, no. 2 (2005): 113–25. http://dx.doi.org/10.1109/tvcg.2005.21.

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18

Falk, M., and D. Weiskopf. "Output-Sensitive 3D Line Integral Convolution." IEEE Transactions on Visualization and Computer Graphics 14, no. 4 (2008): 820–34. http://dx.doi.org/10.1109/tvcg.2008.25.

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19

Jenny, Bernhard. "Terrain generalization with line integral convolution." Cartography and Geographic Information Science 48, no. 1 (2020): 78–92. http://dx.doi.org/10.1080/15230406.2020.1833762.

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20

Li, Pingrun. "Generalized convolution-type singular integral equations." Applied Mathematics and Computation 311 (October 2017): 314–23. http://dx.doi.org/10.1016/j.amc.2017.05.036.

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21

Walter, W., and V. Weckesser. "An integral inequality of convolution type." Aequationes Mathematicae 46, no. 1-2 (1993): 200. http://dx.doi.org/10.1007/bf01834008.

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22

Srivastava, H. M., C. L. Koul, and R. K. Raina. "A class of convolution integral equations." Journal of Mathematical Analysis and Applications 108, no. 1 (1985): 63–72. http://dx.doi.org/10.1016/0022-247x(85)90007-1.

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23

Huffman, Timothy, Chull Park, and David Skoug. "Generalized transforms and convolutions." International Journal of Mathematics and Mathematical Sciences 20, no. 1 (1997): 19–32. http://dx.doi.org/10.1155/s0161171297000045.

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In this paper, using the concept of a generalized Feynman integral, we define a generalized Fourier-Feynman transform and a generalized convolution product. Then for two classes of functionals on Wiener space we obtain several results involving and relating these generalized transforms and convolutions. In particular we show that the generalized transform of the convolution product is a product of transforms. In addition we establish a Parseval's identity for functionals in each of these classes.

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24

CHOU, JYH-HORNG, and ING-RONG HORNG. "Double-shifted Chebyshev series for convolution integral and integral equations." International Journal of Control 42, no. 1 (1985): 225–32. http://dx.doi.org/10.1080/00207178508933358.

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25

Al-Omari, Shrideh Khalaf. "On some variant of a whittaker integral operator and its representative in a class of square integrable Boehmians." Boletim da Sociedade Paranaense de Matemática 38, no. 1 (2018): 173. http://dx.doi.org/10.5269/bspm.v38i1.36468.

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This paper investigates some variant of Whittaker integral operators on a class of square integrable Boehmians. We define convolution products and derive the convolution theorem which substantially satisfy the axioms necessary for generating the Whittaker spaces of Boehmians. Relied on this analysis, we give a definition and properties of the Whittaker integral operator in the class of square integrable Boehmians. The extended Whittaker integral operator, is well-defined, linear and coincides with the classical integral in certain properties.

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26

Gupta, P. K., L. A. Bennett, and A. P. Raiche. "Hybrid calculations of the three‐dimensional electromagnetic response of buried conductors." GEOPHYSICS 52, no. 3 (1987): 301–6. http://dx.doi.org/10.1190/1.1442304.

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The hybrid method for computing the electromagnetic response of a three‐dimensional conductor in a layered, conducting half‐space consists of solving a finite‐element problem in a localized region containing the conductor, and using integral‐equation methods to obtain the fields outside that region. The original scheme obtains the boundary values by iterating between the integral‐equation solution and the finite‐element solution, after making an initial guess based on primary values from the field. A two‐dimensional interpolation scheme is then used to speed the evaluation of the [Formula: see

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27

Huffman, Jason P., and Henry E. Heatherly. "Convolution algebras arising from Sturm-Liouville transforms and applications." International Journal of Mathematics and Mathematical Sciences 27, no. 4 (2001): 221–28. http://dx.doi.org/10.1155/s0161171201010584.

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A regular Sturm-Liouville eigenvalue problem gives rise to a related linear integral transform. Churchill has shown how such an integral transform yields, under certain circumstances, a generalized convolution operation. In this paper, we study the properties of convolution algebras arising in this fashion from a regular Sturm-Liouville problem. We give applications of these convolution algebras for solving certain differential and integral equations, and we outline an operational calculus for classes of such equations.

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28

Mustard, David. "Fractional convolution." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 40, no. 2 (1998): 257–65. http://dx.doi.org/10.1017/s0334270000012509.

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AbstractA continuous one-parameter set of binary operators on L2(R) called fractional convolution operators and which includes those of multiplication and convolution as particular cases is constructed by means of the Condon-Bargmann fractional Fourier transform. A fractional convolution theorem generalizes the standard Fourier convolution theorems and a fractional unit distribution generalizes the unit and delta distributions. Some explicit double-integral formulas for the fractional convolution between two functions are given and the induced operation between their corresponding Wigner distr

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29

Brian, Fisher, and Al-Sihery Fatma. "On the logarithmic integral and the convolution." Mathematica Moravica 20, no. 2 (2016): 7–16. http://dx.doi.org/10.5937/matmor1601007b.

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30

McBride, Adam, H. M. Srivastava, and R. G. Buschman. "Theory and Applications of Convolution Integral Equations." Mathematical Gazette 79, no. 484 (1995): 231. http://dx.doi.org/10.2307/3620110.

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31

Fisher, Brian, and Mustafa Telci. "The Sine Integral And The Neutrix Convolution." Integral Transforms and Special Functions 13, no. 6 (2002): 481–87. http://dx.doi.org/10.1080/10652460213748.

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32

Seeger, Andreas. "Singular integral operators with rough convolution kernels." Journal of the American Mathematical Society 9, no. 1 (1996): 95–105. http://dx.doi.org/10.1090/s0894-0347-96-00185-3.

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33

Bushell, P. J., and W. Okrasinski. "Nonlinear Volterra Integral Equations with Convolution Kernel." Journal of the London Mathematical Society s2-41, no. 3 (1990): 503–10. http://dx.doi.org/10.1112/jlms/s2-41.3.503.

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34

Hoog, F. R. De, and R. S. Anderssen. "Kernel perturbations for Volterra convolution integral equations." Journal of Integral Equations and Applications 22, no. 3 (2010): 427–41. http://dx.doi.org/10.1216/jie-2010-22-3-427.

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35

Fisher, Brian, and Fatma Al-Sirehy. "On the sine integral and the convolution." International Journal of Mathematics and Mathematical Sciences 30, no. 6 (2002): 365–75. http://dx.doi.org/10.1155/s0161171202007834.

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The sine integralSi(λx)and the cosine integralCi(λx)and their associated functionsSi+(λx),Si−(λx),Ci+(λx),Ci−(λx)are defined as locally summable functions on the real line. Some convolutions of these functions andsin(μx),sin+(μx), andsin−(μx)are found.

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36

Turner, James D., Achille Messac, and John L. Junkins. "Finite-time matrix convolution integral sensitivity calculations." Journal of Guidance, Control, and Dynamics 11, no. 5 (1988): 473–75. http://dx.doi.org/10.2514/3.20340.

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37

Tuan, Vu Kim. "Integral Transforms of Fourier Cosine Convolution Type." Journal of Mathematical Analysis and Applications 229, no. 2 (1999): 519–29. http://dx.doi.org/10.1006/jmaa.1998.6177.

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38

MYDLARCZYK, W., and W. OKRASINSKI. "NONLINEAR VOLTERRA INTEGRAL EQUATIONS WITH CONVOLUTION KERNELS." Bulletin of the London Mathematical Society 35, no. 04 (2003): 484–90. http://dx.doi.org/10.1112/s0024609303002170.

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39

Girela, Daniel, and Cristóbal González. "Integral Means Inequalities, Convolution, and Univalent Functions." Journal of Function Spaces 2019 (March 3, 2019): 1–5. http://dx.doi.org/10.1155/2019/7817353.

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We use the Baernstein star-function to investigate several questions about the integral means of the convolution of two analytic functions in the unit disc. The theory of univalent functions plays a basic role in our work.

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40

Kim, Bong Jin, Byoung Soo Kim, and David Skoug. "Integral transforms, convolution products, and first variations." International Journal of Mathematics and Mathematical Sciences 2004, no. 11 (2004): 579–98. http://dx.doi.org/10.1155/s0161171204305260.

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We establish the various relationships that exist among the integral transformℱα,βF, the convolution product(F∗G)α, and the first variationδFfor a class of functionals defined onK[0,T], the space of complex-valued continuous functions on[0,T]which vanish at zero.

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41

Burke, James V., Tim Hoheisel, and Christian Kanzow. "Gradient Consistency for Integral-convolution Smoothing Functions." Set-Valued and Variational Analysis 21, no. 2 (2013): 359–76. http://dx.doi.org/10.1007/s11228-013-0235-6.

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42

Gal, Sorin G. "Convolution-Type Integral Operators in Complex Approximation." Computational Methods and Function Theory 1, no. 2 (2001): 417–32. http://dx.doi.org/10.1007/bf03321000.

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43

Al-Musallam, F., and Vu Kim Tuan. "Integral Transforms Related to a Generalized Convolution." Results in Mathematics 38, no. 3-4 (2000): 197–208. http://dx.doi.org/10.1007/bf03322007.

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44

Brychkov, Yu A., H. J. Glaeske, and O. I. Marichev. "Factorization of integral transformations of convolution type." Journal of Soviet Mathematics 30, no. 3 (1985): 2071–94. http://dx.doi.org/10.1007/bf02105396.

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45

Berg, Lothar. "The asymptotic expansion of a convolution integral." Journal of Computational and Applied Mathematics 41, no. 1-2 (1992): 159–61. http://dx.doi.org/10.1016/0377-0427(92)90245-s.

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46

Van Berkel, C. A. M., and S. J. L. Van Eijndhoven. "Convolution integral equations with Gegenbauer function kernel." Journal of Computational and Applied Mathematics 50, no. 1-3 (1994): 565–74. http://dx.doi.org/10.1016/0377-0427(94)90328-x.

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47

Chung, Hyun, Jae Choi, and Seung Chang. "Conditional integral transforms with related topics on function space." Filomat 26, no. 6 (2012): 1151–62. http://dx.doi.org/10.2298/fil1206151c.

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In this paper we study the conditional integral transform, the conditional convolution product and the first variation of functionals on function space. For our research, we modify the class S? of functionals introduced in [7]. We then give the existences of the conditional integral transform, the conditional convolution product and the first variation for functionals in S?. Finally, we give various relationships and formulas among conditional integral transforms, conditional convolution products and first variations of functionals in S?.

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48

Naylor, D. "On an integral transform." International Journal of Mathematics and Mathematical Sciences 9, no. 2 (1986): 283–92. http://dx.doi.org/10.1155/s0161171286000352.

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This paper establishes properties of a convolution type integral transform whose kernel is a Macdonald type Bessel function of zero order. An inversion formula is developed and the transform is applied to obtain the solution of some related integral equations.

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49

Borkowski, Marcin, and Daria Bugajewska. "Applications of Henstock-Kurzweil integrals on an unbounded interval to differential and integral equations." Mathematica Slovaca 68, no. 1 (2018): 77–88. http://dx.doi.org/10.1515/ms-2017-0082.

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Abstract In this paper we are going to apply the Henstock-Kurzweil integrals defined on an unbounded intervals to differential and integral equations defined on such intervals. To deal with linear differential equations we examine convolution involving functions integrable in Henstock-Kurzweil sense. In the case of nonlinear Hammerstein integral equation as well as Volterra integral equation we look for solutions in the space of functions of bounded variation in the sense of Jordan.

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50

Hanna, Latif A.-M., Maryam Al-Kandari, and Yuri Luchko. "Operational method for solving fractional differential equations with the left-and right-hand sided Erdélyi-Kober fractional derivatives." Fractional Calculus and Applied Analysis 23, no. 1 (2020): 103–25. http://dx.doi.org/10.1515/fca-2020-0004.

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AbstractIn this paper, we first provide a survey of some basic properties of the left-and right-hand sided Erdélyi-Kober fractional integrals and derivatives and introduce their compositions in form of the composed Erdélyi-Kober operators. Then we derive a convolutional representation for the composed Erdélyi-Kober fractional integral in terms of its convolution in the Dimovski sense. For this convolution, we also determine the divisors of zero. These both results are then used for construction of an operational method for solving an initial value problem for a fractional differential equation

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