Cover

Title page

Dedication

Foreword to revised edition

Contents

Part one. Functional analysis

Abstract spaces

Linear transformations

Vector-valued functions

Banach algebras

Analysis in a Banach algebra

Laplace integrals and binomial series

Part two. Basic propoerties 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}(-∞,∞)

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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