Advertisement

© 2017

Topological Vector Spaces and Their Applications

Book

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

  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia

About the authors

Vladimir Bogachev, born in 1961, Professor at the Department of Mechanics and Mathematics of Lomonosov Moscow State University and at the Faculty of Mathematics of the Higher School of Economics (Moscow, Russia) is an expert in measure theory and infinite-dimensional analysis and the author of more than 200 papers and 12 monographs, including his famous two-volume treatise "Measure theory" (Springer, 2007), "Gaussian measures" (AMS, 1997), "Differentiable measures and the Malliavin calculus" (AMS, 2010), "Fokker-Planck-Kolmogorov equations" (AMS, 2015), and others. An author with a high citation index (h=31 with more than 4700 citations according to the Google Scholar), Vladimir Bogachev solved several long-standing problems in measure theory and Fokker-Planck-Kolmogorov equations. 

Oleg Smolyanov, born in 1938, Professor at the Department of Mechanics and Mathematics of Lomonosov Moscow State University is an expert in topological vector spaces and infinite-dimensional analysis and author of more than 200 papers and 5 monographs. Oleg Smolyanov solved several long-standing problems in the theory of topological vector spaces.

Bibliographic information

Industry Sectors
Finance, Business & Banking

Reviews

“The book under review presents an excellent modern treatment of topological linear spaces. Moreover, in contrast to existing monographs on this topic it adds material on applications that are not covered elsewhere. … The book is well written and elucidates basic concepts with a large list of examples.” (Jan Hamhalter, Mathematical Reviews, November, 2017)

“This is indeed a good book, well written, that includes much useful material. The basic theory is presented in a clear, understandable way. Moreover, many recent, important, more specialized results are also included with precise references. This book is recommendable for analysts interested in the modern theory of locally convex spaces and its applications, and especially for those mathematicians who might use differentiation theory on infinite-dimensional spaces or measure theory on topological vector spaces.” (José Bonet, zbMATH 1378.46001, 2018)