Semigroup Theory And Its Applications
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Semigroup Theory and Its Applications
Author: Alfred Hoblitzelle Clifford
language: en
Publisher: Cambridge University Press
Release Date: 1996-05-16
This volume contains survey papers by the invited speakers at the Conference on Semigroup Theory and Its Applications which took place at Tulane University in April, 1994. The authors represent the leading areas of research in semigroup theory and its applications, both to other areas of mathematics and to areas outside mathematics. Included are papers by Gordon Preston surveying Clifford's work on Clifford semigroups and by John Rhodes tracing the influence of Clifford's work on current semigroup theory. Notable among the areas of application are the paper by Jean-Eric Pin on applications of other areas of mathematics to semigroup theory and the paper by the editors on an application of semigroup theory to theoretical computer science and mathematical logic. All workers in semigroup theory will find this volume invaluable.
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. 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.
Semigroups of Linear Operators and Applications to Partial Differential Equations
Author: Amnon Pazy
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
From the reviews: "Since E. Hille and K. Yoshida established the characterization of generators of C0 semigroups in the 1940s, semigroups of linear operators and its neighboring areas have developed into a beautiful abstract theory. Moreover, the fact that mathematically this abstract theory has many direct and important applications in partial differential equations enhances its importance as a necessary discipline in both functional analysis and differential equations. In my opinion Pazy has done an outstanding job in presenting both the abstract theory and basic applications in a clear and interesting manner. The choice and order of the material, the clarity of the proofs, and the overall presentation make this an excellent place for both researchers and students to learn about C0 semigroups." #Bulletin Applied Mathematical Sciences 4/85#1 "In spite of the other monographs on the subject, the reviewer can recommend that of Pazy as being particularly written, with a bias noticeably different from that of the other volumes. Pazy's decision to give a connected account of the applications to partial differential equations in the last two chapters was a particularly happy one, since it enables one to see what the theory can achieve much better than would the insertion of occasional examples. The chapters achieve a very nice balance between being so easy as to appear disappointing, and so sophisticated that they are incomprehensible except to the expert." #Bulletin of the London Mathematical Society#2