Authors:
- Introduces readers to a mathematical crossroads in analysis: semigroups, elliptic boundary value problems and Markov processes
- Presents principal ideas explicitly so that a broad spectrum of readers can easily understand the relationship between partial differential equations and probability in analysis
- Is amply illustrated with 136 figures and 15 tables
- Describes a powerful new method for future research, the Boutet de Monvel calculus
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1499)
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Table of contents (16 chapters)
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Front Matter
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Analytic and Feller Semigroups and Markov Processes
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Front Matter
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Pseudo-Differential Operators and Elliptic Boundary Value Problems
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Front Matter
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Analytic Semigroups in Lp Sobolev Spaces
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Front Matter
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Waldenfels Operators, Boundary Operators and Maximum Principles
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Front Matter
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Feller Semigroups for Elliptic Waldenfels Operators
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Front Matter
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About this book
This 3rd edition provides an insight into the mathematical crossroads formed by functional analysis (the macroscopic approach), partial differential equations (the mesoscopic approach) and probability (the microscopic approach) via the mathematics needed for the hard parts of Markov processes. It brings these three fields of analysis together, providing a comprehensive study of Markov processes from a broad perspective. The material is carefully and effectively explained, resulting in a surprisingly readable account of the subject.
The main focus is on a powerful method for future research in elliptic boundary value problems and Markov processes via semigroups, the Boutet de Monvel calculus. A broad spectrum of readers will easily appreciate the stochastic intuition that this edition conveys. In fact, the book will provide a solid foundation for both researchers and graduate students in pure and applied mathematics interested in functional analysis, partial differential equations, Markov processes and the theory of pseudo-differential operators, a modern version of the classical potential theory.
Reviews
Authors and Affiliations
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Institute of Mathematics, University of Tsukuba, Tsukuba, Japan
Kazuaki Taira
About the author
Kazuaki Taira was a Professor of mathematics at the University of Tsukuba, Japan. He received his Bachelor of Science degree in 1969 from the University of Tokyo and his Master of Science degree in 1972 from the Tokyo Institute of Technology, where he served as an assistant from 1972 to 1978. In 1976 he was awarded the Doctor of Science degree by the University of Tokyo, and in 1978 the Doctorat d'Etat degree by Université de Paris-Sud (Orsay), where he had studied on a French government scholarship (1976–1978).
Taira was also a member of the Institute for Advanced Study (Princeton) (1980–1981), associate professor at the University of Tsukuba (1981–1995), and professor at Hiroshima University (1995–1998). In 1998, he returned to the University of Tsukuba to teach there again as a professor. From 2009 to 2017 he was a part-time professor at Waseda University (Tokyo). His current research interests are in the study of three interrelated subjects in analysis: semigroups, elliptic boundary value problems and Markov processes.
Bibliographic Information
Book Title: Boundary Value Problems and Markov Processes
Book Subtitle: Functional Analysis Methods for Markov Processes
Authors: Kazuaki Taira
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-48788-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-48787-4Published: 02 July 2020
eBook ISBN: 978-3-030-48788-1Published: 01 July 2020
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 3
Number of Pages: XVII, 502
Number of Illustrations: 150 b/w illustrations
Topics: Probability Theory and Stochastic Processes, Analysis, Operator Theory