Polyharmonic functions of infinite order on annular regions

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Title: Polyharmonic functions of infinite order on annular regions
Authors: Kounchev, Ognyan
Render, Hermann
Permanent link: http://hdl.handle.net/10197/5556
Date: Jun-2013
Abstract: Polyharmonic functions f of in nite order and type on annular regions are systematically studied. The rst main result states that the Fourier-Laplace coefficients fk;l (r) of a polyharmonic function f of in nite order and type 0 can be extended to analytic functions on the complex plane cut along the negative semiaxis. The second main result gives a constructive procedure via Fourier-Laplace series for the analytic extension of a polyharmonic function on annular region A(r0; r1) of in nite order and type less than 1=2r1 to the kernel of the harmonicity hull of the annular region. The methods of proof depend on an extensive investigation of Taylor series with respect to linear differential operators with constant coefficients.
Type of material: Journal Article
Publisher: Tohoku University. Mathematical Institute.
Journal: Tohoku Mathematical Journal
Volume: 65
Issue: 2
Start page: 199
End page: 299
Copyright (published version): 2013 Tohoku University. Mathematical Institute.
Keywords: Polyharmonic functionsAnnular regionFourier-Laplace series
Other versions: http://www.math.tohoku.ac.jp/tmj/abs/abs65_2_3.html
Language: en
Status of Item: Peer reviewed
Appears in Collections:Mathematics and Statistics Research Collection

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