**Colloquium Publications**

Volume: 31;
1996;
808 pp;
Softcover

MSC: Primary 57;

Print ISBN: 978-0-8218-1031-6

Product Code: COLL/31

List Price: $69.00

Individual Member Price: $55.20

**Electronic ISBN: 978-0-8218-3395-7
Product Code: COLL/31.E**

List Price: $69.00

Individual Member Price: $55.20

# Functional Analysis and Semi-groups

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*E. Hille; R. S. Phillips*

#### Table of Contents

# Table of Contents

## Functional Analysis and Semi-groups

- Cover Cover11
- Title page iii4
- Dedication v6
- Foreword to revised edition vii8
- Contents ix10
- Part one. Functional analysis 116
- Abstract spaces 217
- Linear transformations 2338
- Vector-valued functions 5873
- Banach algebras 117132
- Analysis in a Banach algebra 164179
- Laplace integrals and binomial series 212227
- Part two. Basic propoerties of semi-groups 236251
- Subadditive functions 237252
- Semi-modules 256271
- Addition theorem in a Banach algebra 277292
- Semi-groups in the strong topology 302317
- Generator and resolvent 337352
- Generation of semi-groups 356371
- Part three. Advanced analytical theory of semi-groups 387402
- Perturbation theory 388403
- Adjoint theory 421436
- Operational calculus 434449
- Spectral theory 453468
- Holomorphic semi-groups 472487
- Applications to ergodic theory 502517
- Part four. Special semi-groups and applications 529544
- Translations and powers 530545
- Trigonometric semi-groups 543558
- Semi-groups in 𝐿_{𝑝}(-∞,∞) 566581
- Semi-groups in Hilbert space 583598
- Miscellaneous applications 606621
- Part five. Extensions of the theory 679694
- Notes on Banach algebras 680695
- Lie semi-groups 726741
- Functions on vectors to vectors 760775
- Bibliography 781796
- Index 797812
- Back Cover Back Cover1825

#### Reviews

This book is devoted to the study of semigroups (associative multiplicative systems for which no cancellation rules are postulated) and their linear representations in Banach spaces. Commutative semigroups receive generous but not exclusive attention.

-- M. H. Stone

This volume is a revised edition, with Phillips as co-author, of the well-known book of Hille under the same title. The revision is a thorough one, involving rearrangement, the addition of new background material, and the incorporation of many new results. Each part and each chapter commences with a summary, and each chapter closes with a short list of general references to the bibliography presented at the end of the book. Other references are liberally supplied in the body of the text. There is an extensive index.

-- Mathematical Reviews