Theory of Semigroups and Applications

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. Manyexamples 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.

Auteur

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.

Contenu

Chapter 1. Vector-valued functions.- Chapter 2. C0-semigroups.- Chapter 3. Dissipative operators and holomorphic semigroups.- Chapter 4. Perturbation and convergence of semigroups.- Chapter 5. Chernoff's Theorem and its applications.- Chapter 6. Markov semigroups.- Chapter 7. Applications to partial differential equations.- Appendix A1. Unbounded operators.- Appendix A2. Fourier transforms.- Appendix A3. Sobolev spaces.