Boundary values and Poisson integral representations
Identifieur interne : 002795 ( Main/Exploration ); précédent : 002794; suivant : 002796Boundary values and Poisson integral representations
Auteurs : Henrik Schlichtkrull [Danemark]Source :
- Progress in Mathematics ; 1984.
Abstract
Abstract: Consider the open disk D = {|z| > 1} in C with the boundary T = {|z| = 1}. The classical Poisson kernel is defined by (5.1) $$ P\left( {z,t} \right) = \tfrac{{1 - {{\left| z \right|}^2}}}{{{{\left| {t - z} \right|}^2}}} $$ for z ∈ D , t ∈ T , and the Poisson transform Pf on D of a function f on T is given by (5.2) $$ Pf(z) = \int {_Tf(t)\;P} \left( {z,t} \right)dt $$
Url:
DOI: 10.1007/978-1-4612-5298-6_5
Affiliations:
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