SEMIGROUPS AND LINEAR OPERATORS
CONTENTS I INTRODUCTION 1 STRONGLY CONTINUOUS SEMIGROUPS A BASIC PROPERTIES B STANDARD CONSTRUCTIONS 2 EXAMPLES A FINITE-DIMENSIONAL SYSTEMS: MATRIX SEMIGROUPS B UNIFORMLY CONTINUOUS OPERATOR SEMIGROUPS 3 MORE SEMIGROUPS A MULTIPLICATION SEMIGROUPS ON C0(?) B MULTIPLICATION SEMIGROUPS ON LP(?, µ) C TRANSLATION SEMIGROUPS II SEMIGROUPS, GENERATORS, AND RESOLVENTS 1 GENERATORS OF SEMIGROUPS AND THEIR RESOLVENTS 2 EXAMPLES REVISITED A STANDARD CONSTRUCTIONS B STANDARD EXAMPLES C SOBOLEV TOWERS 3 GENERATION THEOREMS A HILLE–YOSIDA THEOREMS B THE LUMER–PHILLIPS THEOREM C MORE EXAMPLES 4 ANALYTIC SEMIGROUPS 5 FURTHER REGULARITY PROPERTIES OF SEMIGROUPS 6 WELL-POSEDNESS FOR EVOLUTION EQUATIONS III PERTURBATION OF SEMIGROUPS 1 BOUNDED PERTURBATIONS 2 PERTURBATIONS OF CONTRACTIVE AND ANALYTIC SEMIGROUPS IV APPROXIMATION OF SEMIGROUPS 1 TROTTER–KATO APPROXIMATION THEOREMS A A TECHNICAL TOOL: PSEUDORESOLVENTS B THE APPROXIMATION THEOREMS C EXAMPLES 2 THE CHERNO?PRODUCT FORMULA V SPECTRAL THEORY AND ASYMPTOTICS FOR SEMIGROUPS 1 SPECTRUM OF SEMIGROUPS AND GENERATORS A SPECTRAL THEORY FOR CLOSED OPERATORS B SPECTRAL THEORY FOR GENERATORS 2 SPECTRAL MAPPING THEOREMS A EXAMPLES AND COUNTEREXAMPLES B SPECTRAL MAPPING THEOREMS FOR SEMIGROUPS 3 STABILITY AND HYPERBOLICITY OF SEMIGROUPS A STABILITY CONCEPTS B CHARACTERIZATION OF UNIFORM EXPONENTIAL STABILITY C HYPERBOLIC DECOMPOSITIONS 4 CONVERGENCE TO EQUILIBRIUM VI POSITIVE SEMIGROUPS 1 BASIC PROPERTIES 2 SPECTRAL THEORY FOR POSITIVE SEMIGROUPS 3 CONVERGENCE TO EQUILIBRIUM, REVISITED 4 SEMIGROUPS FOR AGE-DEPENDENT POPULATION EQUATIONS