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Full Product Details

Author:   David Applebaum (University of Sheffield)
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Dimensions:   Width: 15.10cm , Height: 1.40cm , Length: 22.80cm
Weight:   0.350kg
ISBN:  

9781108716376

ISBN 10:   1108716377
Pages:   232
Publication Date:   15 August 2019
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In stock  
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Table of Contents

Introduction; 1. Semigroups and generators; 2. The generation of semigroups; 3. Convolution semigroups of measures; 4. Self adjoint semigroups and unitary groups; 5. Compact and trace class semigroups; 6. Perturbation theory; 7. Markov and Feller semigroups; 8. Semigroups and dynamics; 9. Varopoulos semigroups; Notes and further reading; Appendices: A. The space C0(Rd); B. The Fourier transform; C. Sobolev spaces; D. Probability measures and Kolmogorov's theorem on construction of stochastic processes; E. Absolute continuity, conditional expectation and martingales; F. Stochastic integration and Itô's formula; G. Measures on locally compact spaces: some brief remarks; References; Index.

Reviews

'… Applebaum has written a book that provides substantial depth and rigor, with a plethora of references. A notable feature of the text that increases its appeal is the author's inclusion of applications of the theory of semigroups to partial differential equations, dynamical systems, physics, and probability. This book also includes several advanced topics-such as measure spaces, spectral decompositions, and fractional calculus-but Applebaum offers motivating examples for readers to consider, interesting exercises to increase their comprehension, and additional resources to help them find complete details, so that a student could successfully navigate through this material independently if need be.' M. Clay, Choice 'Overall, this book is an interesting contribution to the semigroup literature which does not follow a standard route.' Eric Stachura, MAA Reviews 'Experts can quickly browse through any of the chapters, and get nicely acquainted with examples they are not yet fully aware of. Students can read this book fairly casually, and gain great motivation to study functional, stochastic, and/or harmonic analysis further. Last but not least, teachers of graduate courses can design several great courses by elaborating on one of the many threads running through the book under review and using the referred sources to turn them into self-contained stories. All will appreciate the book's excellent mix of erudition and pedagogy.' Pierre Portal, MathSciNet 'Some readers will enjoy the topic for its inherent attraction as a means of presenting results in a simple and widely applicable way. A masters student who is interested in researching in analysis but not in technical details of PDEs may nd this text particularly useful for finding a research topic in one of the related areas. In these respects the book achieves the aims declared in its introduction, in a way which is not found in earlier texts.' Charles Batty, The Mathematical Gazette

'... Applebaum has written a book that provides substantial depth and rigor, with a plethora of references. A notable feature of the text that increases its appeal is the author's inclusion of applications of the theory of semigroups to partial differential equations, dynamical systems, physics, and probability. This book also includes several advanced topics-such as measure spaces, spectral decompositions, and fractional calculus-but Applebaum offers motivating examples for readers to consider, interesting exercises to increase their comprehension, and additional resources to help them find complete details, so that a student could successfully navigate through this material independently if need be.' M. Clay, Choice 'Overall, this book is an interesting contribution to the semigroup literature which does not follow a standard route.' Eric Stachura, MAA Reviews 'Experts can quickly browse through any of the chapters, and get nicely acquainted with examples they are not yet fully aware of. Students can read this book fairly casually, and gain great motivation to study functional, stochastic, and/or harmonic analysis further. Last but not least, teachers of graduate courses can design several great courses by elaborating on one of the many threads running through the book under review and using the referred sources to turn them into self-contained stories. All will appreciate the book's excellent mix of erudition and pedagogy.' Pierre Portal, MathSciNet 'Some readers will enjoy the topic for its inherent attraction as a means of presenting results in a simple and widely applicable way. A masters student who is interested in researching in analysis but not in technical details of PDEs may nd this text particularly useful for finding a research topic in one of the related areas. In these respects the book achieves the aims declared in its introduction, in a way which is not found in earlier texts.' Charles Batty, The Mathematical Gazette

'... Applebaum has written a book that provides substantial depth and rigor, with a plethora of references. A notable feature of the text that increases its appeal is the author's inclusion of applications of the theory of semigroups to partial differential equations, dynamical systems, physics, and probability. This book also includes several advanced topics-such as measure spaces, spectral decompositions, and fractional calculus-but Applebaum offers motivating examples for readers to consider, interesting exercises to increase their comprehension, and additional resources to help them find complete details, so that a student could successfully navigate through this material independently if need be.' M. Clay, Choice 'Overall, this book is an interesting contribution to the semigroup literature which does not follow a standard route.' Eric Stachura, MAA Reviews '... Applebaum has written a book that provides substantial depth and rigor, with a plethora of references. A notable feature of the text that increases its appeal is the author's inclusion of applications of the theory of semigroups to partial differential equations, dynamical systems, physics, and probability. This book also includes several advanced topics-such as measure spaces, spectral decompositions, and fractional calculus-but Applebaum offers motivating examples for readers to consider, interesting exercises to increase their comprehension, and additional resources to help them find complete details, so that a student could successfully navigate through this material independently if need be.' M. Clay, Choice 'Overall, this book is an interesting contribution to the semigroup literature which does not follow a standard route.' Eric Stachura, MAA Reviews

Author Information

David Applebaum is Professor of Mathematics at the University of Sheffield. His specialist research area is stochastic analysis, with particular emphasis on analytic and probabilistic aspects of processes with jumps on Lie groups, symmetric spaces and manifolds.

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