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Functional Analysis and Semi-groups
About this Title
E. Hille and R. S. Phillips
Publication: Colloquium Publications
Publication Year:
1996; Volume 31
ISBNs: 978-0-8218-1031-6 (print); 978-0-8218-3395-7 (online)
DOI: https://doi.org/10.1090/coll/031
MathSciNet review: MR0025077
MSC: Primary 46.0X
Table of Contents
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Front/Back Matter
Part one. Functional analysis
- Chapter 1. Abstract spaces
- Chapter 2. Linear transformations
- Chapter 3. Vector-valued functions
- Chapter 4. Banach algebras
- Chapter 5. Analysis in a Banach algebra
- Chapter 6. Laplace integrals and binomial series
Part two. Basic propoerties of semi-groups
- Chapter 7. Subadditive functions
- Chapter 8. Semi-modules
- Chapter 9. Addition theorem in a Banach algebra
- Chapter 10. Semi-groups in the strong topology
- Chapter 11. Generator and resolvent
- Chapter 12. Generation of semi-groups
Part three. Advanced analytical theory of semi-groups
- Chapter 13. Perturbation theory
- Chapter 14. Adjoint theory
- Chapter 15. Operational calculus
- Chapter 16. Spectral theory
- Chapter 17. Holomorphic semi-groups
- Chapter 18. Applications to ergodic theory
Part four. Special semi-groups and applications
- Chapter 19. Translations and powers
- Chapter 20. Trigonometric semi-groups
- Chapter 21. Semi-groups in $L_p(-\infty ,\infty )$
- Chapter 22. Semi-groups in Hilbert space
- Chapter 23. Miscellaneous applications
Part five. Extensions of the theory
- Chapter 24. Notes on Banach algebras
- Chapter 25. Lie semi-groups
- Chapter 26. Functions on vectors to vectors