Bergman kernel, Szegö kernel and Dirichlet integral

DOI10.1007/s11785-023-01409-wMaRDI QIDQ6081656

Akira Yamada

Publication date: 5 October 2023

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

zbMATH Keywords

Bergman kernelintegral transformationreproducing kernelSzegö kernelplanar regular region

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Integral representations; canonical kernels (Szeg?, Bergman, etc.) (32A25)

Cites Work

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• The Dirichlet functional. I
• A characterization of the adjoint L-kernel of Szegö type
• The exact Bergman kernel and the kernels of Szegö type
• Theta functions on Riemann surfaces
• Various types of orthogonalization
• Open Riemann surfaces and extremal problems on compact subregions
• The Dirichlet Norm and the Norm of Szego Type
• Solution of the Problem of Plateau
• Theta functions, kernel functions, and Abelian integrals
• Theory of Reproducing Kernels

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