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Theory of Semigroups and Applications

  • Kalyan B. Sinha
  • Sachi Srivastava

Part of the Texts and Readings in Mathematics book series (TRIM, volume 74)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Kalyan B. Sinha, Sachi Srivastava
    Pages 1-19
  3. Kalyan B. Sinha, Sachi Srivastava
    Pages 21-51
  4. Kalyan B. Sinha, Sachi Srivastava
    Pages 53-79
  5. Kalyan B. Sinha, Sachi Srivastava
    Pages 81-96
  6. Kalyan B. Sinha, Sachi Srivastava
    Pages 97-114
  7. Kalyan B. Sinha, Sachi Srivastava
    Pages 115-135
  8. Kalyan B. Sinha, Sachi Srivastava
    Pages 137-146
  9. Back Matter
    Pages 147-169

About this book

Introduction

The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators.

Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in each chapter, partly to initiate and motivate the theory developed and partly to underscore the applications. The choice of topics in this vastly developed book is a difficult one, and the authors have made an effort to stay closer to applications instead of bringing in too many abstract concepts.

Keywords

Semigroups Bochner integral Hille-Yosida Theorem Holomorphic semigroups Chernoff’s Theorem Markov semigroups Schrodinger equation Fourier transforms Sobolev spaces

Authors and affiliations

  • Kalyan B. Sinha
    • 1
  • Sachi Srivastava
    • 2
  1. 1.Jawaharlal Nehru Centre for Advanced Scientific ResearchBangaloreIndia
  2. 2.Department of MathematicsUniversity of DelhiNew DelhiIndia

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-4864-7
  • Copyright Information Springer Nature Singapore Pte Ltd. 2017 and Hindustan Book Agency 2017 2017
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Online ISBN 978-981-10-4864-7
  • Series Print ISSN 2366-8717
  • Series Online ISSN 2366-8725
  • Buy this book on publisher's site