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Topological Vector Spaces and Their Applications

  • V.I. Bogachev
  • O.G. Smolyanov

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-x
  2. V. I. Bogachev, O. G. Smolyanov
    Pages 1-100
  3. V. I. Bogachev, O. G. Smolyanov
    Pages 101-152
  4. V. I. Bogachev, O. G. Smolyanov
    Pages 153-242
  5. V. I. Bogachev, O. G. Smolyanov
    Pages 243-310
  6. V. I. Bogachev, O. G. Smolyanov
    Pages 311-418
  7. Back Matter
    Pages 419-456

About this book

Introduction

This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. In addition, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. 

The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Keywords

46A03, 58C20, 28C20 Topological vector space Locally convex space Differentiation in infinite-dimensional spaces Integration in infinite-dimensional spaces Measures on infinite-dimensional spaces

Authors and affiliations

  • V.I. Bogachev
    • 1
  • O.G. Smolyanov
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-57117-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-57116-4
  • Online ISBN 978-3-319-57117-1
  • Series Print ISSN 1439-7382
  • Series Online ISSN 2196-9922
  • Buy this book on publisher's site