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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Matrix transformations of power series


Authors: David Borwein and Amnon Jakimovski
Journal: Proc. Amer. Math. Soc. 122 (1994), 511-523
MSC: Primary 47B37; Secondary 30B10, 40C05
MathSciNet review: 1198451
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the sequence of transforms $ ({g_n})$ of a power series $ \sum\nolimits_{n = 0}^\infty {{a_n}{z^n}} $ given by $ {g_n}(z): = \sum\nolimits_{k = 0}^\infty {{b_{nk}}{a_k}{z^k}} $. 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 $ {D_P}: = \{ z:\vert z\vert < P\} $ to a function holomorphic on $ {D_P}$.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1198451-0
PII: S 0002-9939(1994)1198451-0
Keywords: Nörlund, matrix transforms, power series
Article copyright: © Copyright 1994 American Mathematical Society