Analysis I

Convergence, Elementary functions

  • Roger Godement

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Roger Godement
    Pages 1-43
  3. Roger Godement
    Pages 45-185
  4. Roger Godement
    Pages 187-324
  5. Back Matter
    Pages 425-434

About this book

Introduction

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonlinearly, blending rigorous mathematics skilfully with didactical and historical considerations. It sets out to illustrate the variety of possible approaches to the main results, in order to initiate the reader to methods, the underlying reasoning, and fundamental ideas. It is suitable for both teaching and self-study. In his familiar, personal style, the author emphasizes ideas over calculations and, avoiding the condensed style frequently found in textbooks, explains these ideas without parsimony of words. The French edition in four volumes, published from 1998, has met with resounding success: the first two volumes are now available in English.

Keywords

Banach Space Fourier Fourier series analytic functions calculus convergence derivations integrals intermediate value theorem logarithm

Authors and affiliations

  • Roger Godement
    • 1
  1. 1.Département de MathématiquesUniversité Paris VIIParis Cedex 05France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-18491-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2004
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-05923-3
  • Online ISBN 978-3-642-18491-8
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book