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Functional Analysis and Semi-groups

E Hille and R S Phillips
Publisher: 
American Mathematical Society
Publication Date: 
1996
Number of Pages: 
808
Format: 
Paperback
Series: 
Colloquium Publications 31
Price: 
62.00
ISBN: 
9780821810316
Category: 
Monograph
BLL Rating: 

The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

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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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