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Journal articles on the topic 'Szego kernel'

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Author: Grafiati

Published: 10 December 2022

Last updated: 10 March 2023

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1

Francsics, Gabor, and Nicolas Hanges. "Treves curves and the Szego kernel." Indiana University Mathematics Journal 47, no. 3 (1998): 0. http://dx.doi.org/10.1512/iumj.1998.47.1505.

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2

CHUNG, YOUNG-BOK. "THE BERGMAN KERNEL FUNCTION AND THE SZEGO KERNEL FUNCTION." Journal of the Korean Mathematical Society 43, no. 1 (January 1, 2006): 199–213. http://dx.doi.org/10.4134/jkms.2006.43.1.199.

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3

Mccullough, Scott, and Li-Chien Shen. "On the Szego Kernel of an Annulus." Proceedings of the American Mathematical Society 121, no. 4 (August 1994): 1111. http://dx.doi.org/10.2307/2161221.

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4

Kuranishi, Masatake. "THE FORMULA FOR THE SINGULARITY OF SZEGO KERNEL : I." Journal of the Korean Mathematical Society 40, no. 4 (July 1, 2003): 641–66. http://dx.doi.org/10.4134/jkms.2003.40.4.641.

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5

Bell, Steven R. "Simplicity of the Bergman, Szego and Poisson kernel functions." Mathematical Research Letters 2, no. 3 (1995): 267–77. http://dx.doi.org/10.4310/mrl.1995.v2.n3.a4.

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6

Diaz, Katharine Perkins. "The Szego Kernel as a Singular Integral Kernel on a Family of Weakly Pseudoconvex Domains." Transactions of the American Mathematical Society 304, no. 1 (November 1987): 141. http://dx.doi.org/10.2307/2000708.

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7

Francsics, Gabor, and Nicholas Hanges. "Explicit Formulas for the Szego Kernel on Certain Weakly Pseudoconvex Domains." Proceedings of the American Mathematical Society 123, no. 10 (October 1995): 3161. http://dx.doi.org/10.2307/2160676.

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8

Chang, Der-Chen, Xuan Thinh Duong, Ji Li, Wei Wang, and Qingyan Wu. "An explicit formula of Cauchy-Szego kernel for quaternionic Siegel upper half space and applications." Indiana University Mathematics Journal 70, no. 6 (2021): 2451–77. http://dx.doi.org/10.1512/iumj.2021.70.8732.

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9

Speransky, K. S. "On the convergence of the order-preserving weak greedy algorithm for subspaces generated by the Szego kernel in the Hardy space." Izvestia of Saratov University. New Series. Series: Mathematics. Mechanics. Informatics 21, no. 3 (August 25, 2021): 336–42. http://dx.doi.org/10.18500/1816-9791-2021-21-3-336-342.

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10

Gafai, Nuraddeen S., Ali H. M. Murid, and Nur H. A. A. Wahid. "Infinite Product Representation for the Szegö Kernel for an Annulus." Journal of Function Spaces 2022 (April 12, 2022): 1–9. http://dx.doi.org/10.1155/2022/3763450.

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The Szegö kernel has many applications to problems in conformal mapping and satisfies the Kerzman-Stein integral equation. The Szegö kernel for an annulus can be expressed as a bilateral series and has a unique zero. In this paper, we show how to represent the Szegö kernel for an annulus as a basic bilateral series (also known as q -bilateral series). This leads to an infinite product representation through the application of Ramanujan’s sum. The infinite product clearly exhibits the unique zero of the Szegö kernel for an annulus. Its connection with the basic gamma function and modified Jacobi theta function is also presented. The results are extended to the Szegö kernel for general annulus and weighted Szegö kernel. Numerical comparisons on computing the Szegö kernel for an annulus based on the Kerzman-Stein integral equation, the bilateral series, and the infinite product are also presented.

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11

Salzo, Saverio, and Johan A. K. Suykens. "Generalized support vector regression: Duality and tensor-kernel representation." Analysis and Applications 18, no. 01 (December 6, 2019): 149–83. http://dx.doi.org/10.1142/s0219530519410069.

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In this paper, we study the variational problem associated to support vector regression in Banach function spaces. Using the Fenchel–Rockafellar duality theory, we give an explicit formulation of the dual problem as well as of the related optimality conditions. Moreover, we provide a new computational framework for solving the problem which relies on a tensor-kernel representation. This analysis overcomes the typical difficulties connected to learning in Banach spaces. We finally present a large class of tensor-kernels to which our theory fully applies: power series tensor kernels. This type of kernels describes Banach spaces of analytic functions and includes generalizations of the exponential and polynomial kernels as well as, in the complex case, generalizations of the Szegö and Bergman kernels.

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12

Mo, Y., T. Qian, and W. Mi. "Sparse representation in Szegő kernels through reproducing kernel Hilbert space theory with applications." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 04 (July 2015): 1550030. http://dx.doi.org/10.1142/s0219691315500307.

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This paper discusses generalization bounds for complex data learning which serve as a theoretical foundation for complex support vector machine (SVM). Drawn on the generalization bounds, a complex SVM approach based on the Szegő kernel of the Hardy space H2(𝔻) is formulated. It is applied to the frequency-domain identification problem of discrete linear time-invariant system (LTIS). Experiments show that the proposed algorithm is effective in applications.

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13

Felipe, Raúl, and Mauricio García Arroyo. "The discrete Szëgo kernel." Journal of Difference Equations and Applications 14, no. 4 (April 2008): 367–80. http://dx.doi.org/10.1080/10236190701483079.

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14

Wahid, Nur H. A. A., Ali H. M. Murid, and Mukhiddin I. Muminov. "Analytical Solution for Finding the Second Zero of the Ahlfors Map for an Annulus Region." Journal of Mathematics 2019 (August 28, 2019): 1–11. http://dx.doi.org/10.1155/2019/6961476.

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The Ahlfors map is a conformal mapping function that maps a multiply connected region onto a unit disk. It can be written in terms of the Szegö kernel and the Garabedian kernel. In general, a zero of the Ahlfors map can be freely prescribed in a multiply connected region. The remaining zeros are the zeros of the Szegö kernel. For an annulus region, it is known that the second zero of the Ahlfors map can be computed analytically based on the series representation of the Szegö kernel. This paper presents another analytical method for finding the second zero of the Ahlfors map for an annulus region without using the series approach but using a boundary integral equation and knowledge of intersection points.

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15

Paoletti, Roberto. "Scaling limits for equivariant Szego kernels." Journal of Symplectic Geometry 6, no. 1 (2008): 9–32. http://dx.doi.org/10.4310/jsg.2008.v6.n1.a2.

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16

Santos-León, J. C. "Szegö polynomials and Szegö quadrature for the Fejér kernel." Journal of Computational and Applied Mathematics 179, no. 1-2 (July 2005): 327–41. http://dx.doi.org/10.1016/j.cam.2004.09.048.

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17

Speransky, Konstantin Sergeevich, and Pavel AleksandrovichPavel Aleksandrovich Terekhin. "О существовании фреймов в пространстве Харди, построенных на основе ядра Сеге." Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 2 (2019): 57–68. http://dx.doi.org/10.26907/0021-3446-2019-2-57-68.

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18

Wu, JuJie, and Xu Xing. "Boundary behavior of the Szegö kernel." Bulletin of the London Mathematical Society 54, no. 1 (February 2022): 285–300. http://dx.doi.org/10.1112/blms.12623.

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19

Lu, Zhiqin, and Steve Zelditch. "Szegő kernels and Poincaré series." Journal d'Analyse Mathématique 130, no. 1 (November 2016): 167–84. http://dx.doi.org/10.1007/s11854-016-0033-9.

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20

Komatsu, Gen. "Hadamard's variational formula for the Szegő kernel." Kodai Mathematical Journal 8, no. 2 (1985): 157–62. http://dx.doi.org/10.2996/kmj/1138037044.

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21

McCullough, Scott, and Li-Chien Shen. "On the Szegő\ kernel of an annulus." Proceedings of the American Mathematical Society 121, no. 4 (April 1, 1994): 1111. http://dx.doi.org/10.1090/s0002-9939-1994-1189748-9.

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22

Morais, J., K. I. Kou, and W. Sprößig. "Generalized holomorphic Szegö kernel in 3D spheroids." Computers & Mathematics with Applications 65, no. 4 (February 2013): 576–88. http://dx.doi.org/10.1016/j.camwa.2012.10.011.

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23

Chung, Young-Bok, and Moonja Jeong. "The Transformation Formula for the Szegő Kernel." Rocky Mountain Journal of Mathematics 29, no. 2 (June 1999): 463–71. http://dx.doi.org/10.1216/rmjm/1181071646.

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24

Lu, Zhiqin, and Gang Tian. "The log term of the Szegö Kernel." Duke Mathematical Journal 125, no. 2 (November 2004): 351–87. http://dx.doi.org/10.1215/s0012-7094-04-12526-6.

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25

Kerzman, Norberto, and Manfred R. Trummer. "Numerical conformal mapping via the Szegö kernel." Journal of Computational and Applied Mathematics 14, no. 1-2 (February 1986): 111–23. http://dx.doi.org/10.1016/0377-0427(86)90133-0.

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26

Paoletti, Roberto. "The Szegö kernel of a symplectic quotient." Advances in Mathematics 197, no. 2 (November 2005): 523–53. http://dx.doi.org/10.1016/j.aim.2004.10.014.

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27

Rahman, Gauhar, Kottakkaran Sooppy Nisar, Thabet Abdeljawad, and Muhammad Samraiz. "Some New Tempered Fractional Pólya-Szegö and Chebyshev-Type Inequalities with Respect to Another Function." Journal of Mathematics 2020 (November 1, 2020): 1–14. http://dx.doi.org/10.1155/2020/9858671.

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In this present article, we establish certain new Pólya–Szegö-type tempered fractional integral inequalities by considering the generalized tempered fractional integral concerning another function Ψ in the kernel. We then prove certain new Chebyshev-type tempered fractional integral inequalities for the said operator with the help of newly established Pólya–Szegö-type tempered fractional integral inequalities. Also, some new particular cases in the sense of classical tempered fractional integrals are discussed. Additionally, examples of constructing bounded functions are considered. Furthermore, one can easily form new inequalities for Katugampola fractional integrals, generalized Riemann–Liouville fractional integral concerning another function Ψ in the kernel, and generalized fractional conformable integral by applying different conditions.

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28

Machedon, Matei. "Szego Kernels on Pseudoconvex Domains with One Degenerate Eigenvalue." Annals of Mathematics 128, no. 3 (November 1988): 619. http://dx.doi.org/10.2307/1971438.

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29

Paoletti, Roberto. "Szegö kernels and finite group actions." Transactions of the American Mathematical Society 356, no. 8 (November 4, 2003): 3069–76. http://dx.doi.org/10.1090/s0002-9947-03-03490-1.

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30

Paoletti, Roberto. "Moment Maps and Equivariant Szegö Kernels." Journal of Symplectic Geometry 2, no. 1 (2004): 133–75. http://dx.doi.org/10.4310/jsg.2004.v2.n1.a5.

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31

Barchini, L. "Szegö Kernels Associated with Zuckerman Modules." Journal of Functional Analysis 131, no. 1 (July 1995): 145–82. http://dx.doi.org/10.1006/jfan.1995.1086.

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32

Chung, Young-Bok. "THE GREEN FUNCTION AND THE SZEGŐ KERNEL FUNCTION." Honam Mathematical Journal 36, no. 3 (September 25, 2014): 659–68. http://dx.doi.org/10.5831/hmj.2014.36.3.659.

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33

Bolt, Michael. "Szegő kernel transformation law for proper holomorphic mappings." Rocky Mountain Journal of Mathematics 44, no. 3 (June 2014): 779–90. http://dx.doi.org/10.1216/rmj-2014-44-3-779.

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34

Galasso, Andrea, and Roberto Paoletti. "Hamiltonian U(2)-actions and Szegö kernel asymptotics." Journal of Physics: Conference Series 1194 (April 2019): 012035. http://dx.doi.org/10.1088/1742-6596/1194/1/012035.

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35

Tuite, Michael P., and Alexander Zuevsky. "The Szegő Kernel on a Sewn Riemann Surface." Communications in Mathematical Physics 306, no. 3 (July 30, 2011): 617–45. http://dx.doi.org/10.1007/s00220-011-1310-1.

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36

HE, Fuli, Min KU, and Uwe KÄHLER. "Szegö kernel for hardy space of matrix functions." Acta Mathematica Scientia 36, no. 1 (January 2016): 203–14. http://dx.doi.org/10.1016/s0252-9602(15)30088-6.

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37

Chang, D. C., and S. Grellier. "Estimates for the Szegö Kernel on Decoupled Domains." Journal of Mathematical Analysis and Applications 187, no. 2 (October 1994): 628–49. http://dx.doi.org/10.1006/jmaa.1994.1379.

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38

Chung, Y. B. "The Robin Function and the Szegő Kernel Function." Journal of Mathematical Analysis and Applications 192, no. 1 (May 1995): 31–40. http://dx.doi.org/10.1006/jmaa.1995.1158.

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39

Arezzo, Claudio, Andrea Loi, and Fabio Zuddas. "Szegö kernel, regular quantizations and spherical CR-structures." Mathematische Zeitschrift 275, no. 3-4 (May 17, 2013): 1207–16. http://dx.doi.org/10.1007/s00209-013-1178-1.

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40

Loi, Andrea, Daria Uccheddu, and Michela Zedda. "On the Szegö kernel of Cartan–Hartogs domains." Arkiv för Matematik 54, no. 2 (October 2016): 473–84. http://dx.doi.org/10.1007/s11512-015-0228-9.

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41

Paoletti, Roberto. "Szegö Kernels and Asymptotic Expansions for Legendre Polynomials." Journal of Complex Analysis 2017 (October 31, 2017): 1–13. http://dx.doi.org/10.1155/2017/7823545.

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We present a geometric approach to the asymptotics of the Legendre polynomials Pk,n+1, based on the Szegö kernel of the Fermat quadric hypersurface, leading to complete asymptotic expansions holding on expanding subintervals of [-1,1].

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42

Nagel, A., J. P. Rosay, E. M. Stein, and S. Wainger. "Estimates for the Bergman and Szego Kernels in C 2." Annals of Mathematics 129, no. 1 (January 1989): 113. http://dx.doi.org/10.2307/1971487.

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43

Chen, Bo-Yong, and Siqi Fu. "Comparison of the Bergman and Szegö kernels." Advances in Mathematics 228, no. 4 (November 2011): 2366–84. http://dx.doi.org/10.1016/j.aim.2011.07.013.

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44

Żynda, T. Ł. "On Weights Which Admit Reproducing Kernel of Szegő Type." Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) 55, no. 5 (September 2020): 320–27. http://dx.doi.org/10.3103/s1068362320050064.

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45

Gilliam, Michael, and Jennifer Halfpap. "The Szegö kernel for nonpseudoconvex tube domains in ℂ2." Complex Variables and Elliptic Equations 59, no. 6 (June 26, 2013): 769–86. http://dx.doi.org/10.1080/17476933.2013.783026.

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46

Pritsker, Igor E. "Approximation of Conformal Mapping via the Szegő Kernel Method." Computational Methods and Function Theory 3, no. 1 (March 2004): 79–94. http://dx.doi.org/10.1007/bf03321026.

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47

Kuranisha, Masatake. "The Formula for the Singularity of Szegö Kernel: II." Asian Journal of Mathematics 8, no. 2 (2004): 353–62. http://dx.doi.org/10.4310/ajm.2004.v8.n2.a8.

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48

Chung, Young-Bok. "The szegő kernel function of a multiply connected domain." Complex Variables, Theory and Application: An International Journal 32, no. 4 (July 1997): 355–61. http://dx.doi.org/10.1080/17476939708815002.

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49

Tegtmeyer, Thomas J., and Anthony D. Thomas. "The Ahlfors Map and Szegő Kernel for an Annulus." Rocky Mountain Journal of Mathematics 29, no. 2 (June 1999): 709–23. http://dx.doi.org/10.1216/rmjm/1181071660.

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50

Hsiao, Chin-Yu, and George Marinescu. "Szegö kernel asymptotics and Morse inequalities on CR manifolds." Mathematische Zeitschrift 271, no. 1-2 (May 5, 2011): 509–53. http://dx.doi.org/10.1007/s00209-011-0875-x.

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