POLYHARMONIC FUNCTIONS OF INFINITE ORDER ON ANNULAR REGIONS
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- KOUNCHEV OGNYAN
- Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
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- RENDER HERMANN
- School of Mathematical Sciences, University College Dublin
Description
Polyharmonic functions $f$ of infinite order and type $\tau$ on annular regions are systematically studied. The first main result states that the Fourier-Laplace 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 Fourier-Laplace 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.
Journal
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- Tohoku Mathematical Journal, Second Series
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Tohoku Mathematical Journal, Second Series 65 (2), 199-229, 2013
Mathematical Institute, Tohoku University
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Keywords
Details 詳細情報について
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- CRID
- 1390282680093791872
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- NII Article ID
- 130005562145
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- ISSN
- 2186585X
- 00408735
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- Text Lang
- en
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- Data Source
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- JaLC
- Crossref
- CiNii Articles
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- Abstract License Flag
- Disallowed
