Polyharmonic functions of infinite order on annular regions
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|Title:||Polyharmonic functions of infinite order on annular regions||Authors:||Kounchev, Ognyan
|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 functions; Annular region; Fourier-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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