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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
抄録
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.
収録刊行物
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- Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ
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Ｔｏｈｏｋｕ Ｍａｔｈｅｍａｔｉｃａｌ Ｊｏｕｒｎａｌ， Ｓｅｃｏｎｄ Ｓｅｒｉｅｓ 65 (2), 199-229, 2013
東北大学大学院理学研究科数学専攻
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詳細情報 詳細情報について
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- CRID
- 1390282680093791872
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- NII論文ID
- 130005562145
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- ISSN
- 2186585X
- 00408735
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- 本文言語コード
- en
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- データソース種別
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- JaLC
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- 使用不可