A theorem of nehari revisited
作者:
A. Zayed,
M. Freund,
E. Görlich,
期刊:
Complex Variables, Theory and Application: An International Journal
(Taylor Available online 1988)
卷期:
Volume 10,
issue 1
页码: 11-22
ISSN:0278-1077
年代: 1988
DOI:10.1080/17476938808814283
出版商: Gordon and Breach Science Publishers
关键词: Generalized Faber expansion;singularities;analytic continuation;ultraspherical expansion;30B40;41A58
数据来源: Taylor
摘要:
A well-known theorem of Z. Nehari shows how one can locate the singular points of a functionf(z) given bywherepn(z) is the Legendre polynomial of degreen, by relating them to the singular points of the associated functiong(w) given by. This theorem was later generalized by R. Gilbert to the case where, where Cλn(Z) is the ultraspherical polynomial of degreen. In this paper we show a connection between the theory of generalized Faber expansions and the work of Gilbert and Nehari. In fact, we derive theorem for the generalized Faber expansions from which both Nehar' results follow as special cases.
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