Texts and Readings in Mathematics

Theory of Semigroups and Applications

Authors: Sinha, Kalyan, Srivastava, Sachi

  • Discusses major topics in semigroups and applications
  • Emphasises on the explorations of the contact areas and interfaces
  • Contains text arose out of the notes of the lectures given by authors
  • Bridges gaps between theory and applications
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  • ISBN 978-981-10-4864-7
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About this Textbook

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.

About the authors

KALYAN BIDHAN SINHA is professor and the SERB-fellow at the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), and at the Indian Institute of Science (IISc), Bengaluru. Professor Sinha is an Indian mathematician who specialised in mathematical theory of scattering, spectral theory of Schrödinger operators, and quantum stochastic processes. He was awarded in 1988 the Shanti Swarup Bhatnagar Prize for Science and Technology, the highest science award in India, in the mathematical sciences category. A Fellow of the Indian Academy of Science (IASc), Bengaluru, Indian National Science Academy (INSA), New Delhi, and The World Academy of Sciences (TWAS), Italy, he completed his PhD from the University of Rochester, New York, U.S.A.

SACHI SRIVASTAVA is associate professor at the Department of Mathematics, University of Delhi, India. She obtained her DPhil degree from Oxford University, UK and the MTech degree from the University of Delhi, India. Her areas of interest are functional analysis, operator theory, abstract differential equations, operator algebras. She is also a life member of the American Mathematical Society and Ramanujan Mathematical Society.

Table of contents (7 chapters)

  • Vector-Valued Functions

    Sinha, Kalyan B. (et al.)

    Pages 1-19

  • $$C_o$$ -semigroups

    Sinha, Kalyan B. (et al.)

    Pages 21-51

  • Dissipative Operators and Holomorphic Semigroups

    Sinha, Kalyan B. (et al.)

    Pages 53-79

  • Perturbation and Convergence of Semigroups

    Sinha, Kalyan B. (et al.)

    Pages 81-96

  • Chernoff’s Theorem and its Applications

    Sinha, Kalyan B. (et al.)

    Pages 97-114

Buy this book

eBook $55.99
price for USA (gross)
  • ISBN 978-981-10-4864-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
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Bibliographic Information

Bibliographic Information
Book Title
Theory of Semigroups and Applications
Authors
Series Title
Texts and Readings in Mathematics
Series Volume
74
Copyright
2017
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd. 2017 and Hindustan Book Agency 2017
eBook ISBN
978-981-10-4864-7
DOI
10.1007/978-981-10-4864-7
Series ISSN
2366-8717
Edition Number
1
Number of Pages
XII, 169
Number of Illustrations and Tables
1 b/w illustrations
Topics