Contact｜Sitemap｜HOME｜Japanese
HOME > Table of Contents and Abstracts > Vol. 65, No. 2
Tohoku Mathematical Journal
2013
June
SECOND SERIES VOL. 65, NO. 2
Tohoku Math. J.
65 (2013), 199229

Title
POLYHARMONIC FUNCTIONS OF INFINITE ORDER ON ANNULAR REGIONS
Author
Ognyan Kounchev and Hermann Render
(Received April 12, 2011, revised July 23, 2012) 
Abstract.
Polyharmonic functions $f$ of infinite order and type $\tau$ on annular regions are systematically studied. The first main result states that the FourierLaplace coefficients $f_{k,l}(r)$ of a polyharmonic function $f$ of infinite 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 FourierLaplace series for the analytic extension of a polyharmonic function on annular region $A(r_{0},r_{1})$ of infinite order and type less than $1/2r_{1}$ 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.
Mathematics Subject Classification.
Primary 31B30; Secondary 32A07, 42C15.
Key words and phrases.
Polyharmonic function, annular region, FourierLaplace series, Linear differential operator with constant coefficient, Taylor series, analytical extension.


To the top of this page
Back to the Contents