Basic Theory of One-Parameter Semigroups

Derek W. Robinson

Volume 2 in the Proceedings of the Centre for Mathematical Analysis

Preface

The following notes represent a course of lectures delivered at the Australian National University in the second semester of 1982 as part of the mathematics honours programme. Most of the material contained in the notes is standard although a few new refinements and variations are included. The course consisted of twenty six one-hour lectures and this sufficed to present about ninety five per cent of the content of the notes.

I am indebted to Mayda Shahinian of the University of New South Wales for typing a first draft of part of these notes and to Helen Daish of the Australian National University for typing the final draft.

Contents

	Preface	1
1.1	Introduction	2
1.2	Semigroups and Generators	8
1.3	Generators and Semigroups	21
1.4	Norm-dissipative Operators	43
1.5	C0*-semigroups	57
1.6	Analytic Vectors	68
1.7	Holomorphic Semigroups	79
1.8	Convergence of Semigroups	89
1.9	Perturbation Theory	112
1.10	Comparison of Semigroups	125