| 书目名称 | Polynomial Expansions of Analytic Functions | | 副标题 | Reihe: Moderne Funkt | | 编辑 | Ralph P. Boas,R. Creighton Buck | | 视频video | | | 丛书名称 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge | | 图书封面 |  | | 描述 | This monograph deals with the expansion properties, in the complex domain, of sets of polynomials which are defined by generating relations. It thus represents a synthesis of two branches of analysis which have been developing almost independently. On the one hand there has grown up a body of results dealing with the more or less formal prop erties of sets of polynomials which possess simple generating relations. Much of this material is summarized in the Bateman compendia (ERDELYI [1J, vol. III, chap. 19) and in TRUESDELL [1J. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function j(z) as a series 2::CnPn(z), where {Pn} is a prescribed sequence of functions, and the connections between the function j and the coefficients en. BIEBERBACH‘S mono graph Analytisehe Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice Pn (z) = zn, and illustrates the depth and detail which such a specializa tion allows. However, the wealth of available information about other sets of polynomials has seldom been put to work in this connection (the applica | | 出版日期 | Book 19581st edition | | 关键词 | Analytic Functions; Complex analysis; Funktionentheorie; analytic function; function; mathematics | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-87887-9 | | isbn_ebook | 978-3-642-87887-9 | | copyright | Springer-Verlag OHG. Berlin · Göttingen · Heidelberg 1958 |
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发表于 2025-3-21 17:50:55
