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Functional Analysis and Semi-groups
E Hille and R S Phillips
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Colloquium Publications
1996; 808 pp; softcover
Volume: 31
ISBN-10: 0-8218-1031-6
ISBN-13: 978-0-8218-1031-6
List Price: US$65
Member Price: US$52
Order Code: COLL/31
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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

Table of Contents

Part One. Functional Analysis
  • Abstract spaces
  • Linear transformations
  • Vector-valued functions
  • Banach algebras
  • General properties
  • Analysis in a Banach algebra
  • Laplace integrals and binomial series
Part Two. Basic Properties of Semi-Groups
  • Subadditive functions
  • Semi-modules
  • Addition theorem in a Banach algebra
  • Semi-groups in the strong topology
  • Generator and resolvent
  • Generation of semi-groups
Part Three. Advanced Analytical Theory of Semi-Groups
  • Perturbation theory
  • Adjoint theory
  • Operational calculus
  • Spectral theory
  • Holomorphic semi-groups
  • Applications to ergodic theory
Part Four. Special Semi-groups and Applications
  • Translations and powers
  • Trigonometric semi-groups
  • Semi-groups in \(L_p(-\infty ,\infty )\)
  • Semi-groups in Hilbert space
  • Miscellaneous applications
Part Five. Extensions of the theory
  • Notes on Banach algebras
  • Lie semi-groups
  • Functions on vectors to vectors
  • Bibliography
  • Index
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