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Algebraic Formulas for Kernel Functions on Representative Two-Connected Domains

<p>We write down explicit algebraic formulas for the Szeg\H{o}, Garabedian and Bergman kernels for specific two-connected planar domains. We use these results to derive integral representations for a biholomorphic invariant relating the Bergman and Szeg\H{o} kernels. We use the formulas to study the asymptotic behavior of these kernels as a family of two-connected domains approaches the unit disc. We derive an explicit formula for the Green's function for the Laplacian for special values on two-connected domains. Every two-connected domain is biholomorphic to a unique two-connected domain of the type we consider. This allows one to write down formulas for the kernel functions on a general two-connected domain.</p>

  1. 10.25394/pgs.21671978.v1
Identiferoai:union.ndltd.org:purdue.edu/oai:figshare.com:article/21671978
Date06 December 2022
CreatorsRaymond Leonard Polak III (14213096)
Source SetsPurdue University
Detected LanguageEnglish
TypeText, Thesis
RightsCC BY 4.0
Relationhttps://figshare.com/articles/thesis/Algebraic_Formulas_for_Kernel_Functions_on_Representative_Two-Connected_Domains/21671978

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