One-parameter semigroups
Author(s)
Bibliographic Information
One-parameter semigroups
（CWI monograph, 5）
North-Holland, 1987
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Note
Bibliography: p. [301]-308
Includes index
Description and Table of Contents
Description
The theory of semigroups of operators was initiated by E. Hille in his monograph ``Functional Analysis and Semigroups'' which appeared in 1948. In the years thereafter the theory was developed further by W. Feller, T. Kato, R.S. Phillips, K. Yosida and many others. The possible range of applications is enormous and includes problems in mathematical physics, probability theory and control theory. The purpose of this book is to illustrate the richness of the theory of one-parameter semigroups by examining some of its various aspects. It is written in such a way that all three parts can be read more or less independently; it is assumed that the reader is familiar with some of the basic principles of functional analysis.
Table of Contents
- 1. Introduction. I. Contraction Semigroups. 2. Nonlinear Contraction Semigroups and Dissipative Operators (Ph. Clement). 3. Generation of Linear Semigroups (Ph. Clement
- Section 3.5 by H.J.A.M. Heijmans). 4. L 1 -Semigroup Theory of Nonlinear Diffusion (C.J. van Duijn). II. Analytic Semigroups. 5. The Calculus of Analytic Semigroups (S. Angenent). 6. Interpolation and Maximal Regularity (S. Angenent). III. Positive Semigroups. 7. Generators of Positive Semigroups (B. de Pagter). 8. Perron-Frobenius Theory for Positive Semigroups (H.J.A.M. Heijmans). 9. Asymptotic Behaviour (H.J.A.M. Heijmans and B. de Pagter). 10. Two Examples from Structured Population Dynamics (H.J.A.M. Heijmans). Appendices: Convex Functions (B. de Pagter). Ordered Banach Spaces (B. de Pagter). Some Results from Spectral Theory (H.J.A.M. Heijmans). Bibliographical Notes. Bibliography. Index.
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