Geometric Interpretation of the Two Dimensional Poisson Kernel And Its Applications

Title: Geometric Interpretation of the Two Dimensional Poisson Kernel And Its Applications
Identifier: d_2009_2013:ef7fadf792b7:10832
identifier: 11201
Creator: Artamoshin, Sergei,
Contributor: Jozef Dodziuk
Date: 2011
Language: English
Publisher: City University of New York.
Subject: Mathematics | Theoretical mathematics | dirichlet eigenvalue problem | estimation eigenvalues | Geometric Interpretation | hyperbolic laplacian | hyperbolic radial eigenfunction | Poisson Kernel
Abstract: Hermann Schwarz, while studying complex analysis, introduced the geometric interpretation for the Poisson kernel in 1890. We shall see here that the geometric interpretation can be useful to develop a new approach to some old classical problems as well as to obtain several new results, mostly related to hyperbolic geometry.;For example, we obtain One Radius Theorem saying that any two radial eigenfunctions of a Hyperbolic Laplacian assuming the value 1 at the origin can not assume any other common value within some interval [0, p], where the length of this interval depends only on the location of the eigenvalues on the complex plane and does not depend on the distance between them.
Type: dissertation
Source: 2009_2013.csv
degree: Ph.D.
Program: Mathematics

Media: Geometric Interpretation of the Two Dimensional Poisson Kernel And Its Applications