Colloquium Publications 1996; 808 pp; softcover Volume: 31 ISBN10: 0821810316 ISBN13: 9780821810316 List Price: US$65 Member Price: US$52 Order Code: COLL/31
 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 coauthor, of the wellknown 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
 Vectorvalued functions
 Banach algebras
 General properties
 Analysis in a Banach algebra
 Laplace integrals and binomial series
Part Two. Basic Properties of SemiGroups  Subadditive functions
 Semimodules
 Addition theorem in a Banach algebra
 Semigroups in the strong topology
 Generator and resolvent
 Generation of semigroups
Part Three. Advanced Analytical Theory of SemiGroups  Perturbation theory
 Adjoint theory
 Operational calculus
 Spectral theory
 Holomorphic semigroups
 Applications to ergodic theory
Part Four. Special Semigroups and Applications  Translations and powers
 Trigonometric semigroups
 Semigroups in \(L_p(\infty ,\infty )\)
 Semigroups in Hilbert space
 Miscellaneous applications
Part Five. Extensions of the theory  Notes on Banach algebras
 Lie semigroups
 Functions on vectors to vectors
 Bibliography
 Index
