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Polynomial expansions of analytic functions

  • Book
  • © 1964

Overview

Authors:
  1. Ralph P. Boas

    1. Evanston, USA

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    You can also search for this author in PubMed   Google Scholar

  2. R. Creighton Buck

    1. Madison, USA

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Part of the book series: Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge (MATHE1, volume 19)

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Table of contents (4 chapters)

  1. Front Matter

    Pages II-VIII
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  2. Introduction

    • Ralph P. Boas Jr., R. Creighton Buck
    Pages 1-21

  3. Representation of entire functions

    • Ralph P. Boas Jr., R. Creighton Buck
    Pages 21-47

  4. Representation of functions that are regular at the origin

    • Ralph P. Boas Jr., R. Creighton Buck
    Pages 47-65

  5. Applications

    • Ralph P. Boas Jr., R. Creighton Buck
    Pages 65-71

  6. Back Matter

    Pages 71-77
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Keywords

About this book

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 [1], voi. III, chap. 19) and in TRUESDELL [1]. On the other hand, a problem of fundamental interest in classical analysis is to study the representability of an analytic function f(z) as a series ,Lc,. p,. (z), where {p,. } is a prescribed sequence of functions, and the connections between the function f and the coefficients c,. . BIEBERBACH's mono­ graph Analytische Fortsetzung (Ergebnisse der Mathematik, new series, no. 3) can be regarded as a study of this problem for the special choice p,. (z) =z", 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 application of generating relations to expansion of functions is not even mentioned in the Bateman compendia). At the other extreme, J. M.

Authors and Affiliations

  • Evanston, USA

    Ralph P. Boas

  • Madison, USA

    R. Creighton Buck

Bibliographic Information

  • Book Title: Polynomial expansions of analytic functions

  • Authors: Ralph P. Boas, R. Creighton Buck

  • Series Title: Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folge

  • DOI: https://doi.org/10.1007/978-3-662-25170-6

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1964

  • Softcover ISBN: 978-3-662-23179-1Published: 01 January 1964

  • eBook ISBN: 978-3-662-25170-6Published: 29 June 2013

  • Edition Number: 2

  • Number of Pages: VIII, 77

  • Number of Illustrations: 15 b/w illustrations

  • Topics: Functional Analysis, Analysis

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