Matrix transformations of power series

David Orwein; Amnon Jakimovski

doi:10.1090/S0002-9939-1994-1198451-0

Matrix transformations of power series

David Orwein, Amnon Jakimovski

School of Mathematical Sciences

Western University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We consider the sequence of transforms {g_n) of a power series. We establish necessary and sufficient conditions on the matrix (b_nk) for the sequence (g_n) to converge uniformly on compact subsets of the disk Dp:= {z: |z| < P} to a function holomorphic on Dp.

Original language	English
Pages (from-to)	511-523
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	122
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-1994-1198451-0
State	Published - Oct 1994

Keywords

Matrix transforms
Norlund
Power series

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abstract = "We consider the sequence of transforms \{gn) of a power series. We establish necessary and sufficient conditions on the matrix (bnk) for the sequence (gn) to converge uniformly on compact subsets of the disk Dp:= \{z: |z| < P\} to a function holomorphic on Dp.",

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author = "David Orwein and Amnon Jakimovski",

year = "1994",

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AB - We consider the sequence of transforms {gn) of a power series. We establish necessary and sufficient conditions on the matrix (bnk) for the sequence (gn) to converge uniformly on compact subsets of the disk Dp:= {z: |z| < P} to a function holomorphic on Dp.

KW - Matrix transforms

KW - Norlund

KW - Power series

UR - https://www.scopus.com/pages/publications/84966212309

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AN - SCOPUS:84966212309

SN - 0002-9939

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EP - 523

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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Matrix transformations of power series

Abstract

Keywords

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