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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

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Table of Contents

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Front/Back Matter

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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