Cylindrical Poisson kernel method and its applications

Foundations of the modified Poisson kernel method were laid out by Finkelstein and Scheinberg in 1975 in the context of explicit solvability for the adaptive Dirichlet problem in a half plane. Over the past decade, this method has been further developed, and new applications have appeared both in th...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2021-10, Vol.72 (5), Article 176
Main Author: Qiao, Lei
Format: Article
Language:English
Subjects:
Dirichlet problem
Engineering
Fourier analysis
Harmonic analysis
Harmonic functions
Kernels
Mathematical Methods in Physics
Operators (mathematics)
Theoretical and Applied Mechanics
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Summary:Foundations of the modified Poisson kernel method were laid out by Finkelstein and Scheinberg in 1975 in the context of explicit solvability for the adaptive Dirichlet problem in a half plane. Over the past decade, this method has been further developed, and new applications have appeared both in the field of harmonic analysis and operator theory and in practical Schrödinger problems. In this paper, we pay special attention to cylindrical Poisson kernel method’s application for the integral representations of harmonic functions in a cylinder.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-021-01605-8