Existence families, functional calculi, and evolution equations /
This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of op...
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| Format: | eBook |
| Language: | English |
| Published: |
Berlin ; New York :
Springer-Verlag,
[1994]
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| Series: | Lecture notes in mathematics (Springer-Verlag) ;
1570. |
| Subjects: | |
| Online Access: | Connect to the full text of this electronic book |
| Summary: | This book presents an operator-theoretic approach to ill-posed evolution equations. It presents the basic theory, and the more surprising examples, of generalizations of strongly continuous semigroups known as 'existent families' and 'regularized semigroups'. These families of operators may be used either to produce all initial data for which a solution in the original space exists, or to construct a maximal subspace on which the problem is well-posed. Regularized semigroups are also used to construct functional, or operational, calculi for unbounded operators. The book takes an intuitive and constructive approach by emphasizing the interaction between functional calculus constructions and evolution equations. One thinks of a semigroup generated by A as etA and thinks of a regularized semigroup generated by A as etA g(A), producing solutions of the abstract Cauchy problem for initial data in the image of g(A). Material that is scattered throughout numerous papers is brought together and presented in a fresh, organized way, together with a great deal of new material. |
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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xv, 234 pages) |
| Format: | Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. |
| Bibliography: | Includes bibliographical references (pages 218-227). |
| ISBN: | 9783540483229 (electronic bk.) 3540483225 (electronic bk.) |
| ISSN: | 0075-8434 ; |