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© 2011

Global and Stochastic Analysis with Applications to Mathematical Physics

  • Covers branches of mathematics previously absent in monograph form

  • Combines methods of Global and Stochastic Analysis, enabling a more or less common treatment for areas of mathematical physics traditionally considered as divergent

  • Includes substantial background material on manifolds and stochastic analysis, in addition to new work on set-valued mappings and applications of Nelson's mean derivatives

Book

Part of the Theoretical and Mathematical Physics book series (TMP)

Table of contents

  1. Front Matter
    Pages I-XXIII
  2. Global Analysis

    1. Front Matter
      Pages 1-1
    2. Yuri E. Gliklikh
      Pages 3-34
    3. Yuri E. Gliklikh
      Pages 35-66
    4. Yuri E. Gliklikh
      Pages 67-96
    5. Yuri E. Gliklikh
      Pages 97-104
    6. Yuri E. Gliklikh
      Pages 105-112
  3. Stochastic Analysis

    1. Front Matter
      Pages 113-113
    2. Yuri E. Gliklikh
      Pages 139-186
    3. Yuri E. Gliklikh
      Pages 187-224
    4. Yuri E. Gliklikh
      Pages 225-246
    5. Yuri E. Gliklikh
      Pages 247-252
  4. Applications to Mathematical Physics

    1. Front Matter
      Pages 253-253
    2. Yuri E. Gliklikh
      Pages 255-282
    3. Yuri E. Gliklikh
      Pages 299-330
    4. Yuri E. Gliklikh
      Pages 331-354
    5. Yuri E. Gliklikh
      Pages 355-386
    6. Yuri E. Gliklikh
      Pages 387-414

About this book

Introduction

Methods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems

This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation

Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics

A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics

Keywords

Global Analysis Manifolds Nelson's mean derivatives Set-valued mappings Stochastic Analysis

Authors and affiliations

  1. 1.Mathematics DepartmentVoronezh State UniversityVoronezhRussian Federation

Bibliographic information

Reviews

From the reviews:

“The book is about applications of global and stochastic analysis in mathematical physics. The majority of the book reflects the work and contributions of the author and his collaborators in this field. … The author, by putting various preparation materials together, has done a good job presenting the theory in a book that for the most part is quite readable. The book is a valuable contribution to the literature, and is recommended to anyone … who is interested in problems of mathematical physics.” (Ming Liao, Mathematical Reviews, Issue 2012 d)