- Print ISBN 9780444512888
- Electronic ISBN 9780080530048
The book is primarily addressed to graduate students and researchers in the field, but it would be of interest for both physicists and engineers. It should be emphasised that it is almost self-contained, requiring only a basic course in Functional Analysis and Partial Differential Equations.
Chapter 1. Preliminaries.
1.1 Vector-Valued Measurable Functions.
1.2 The Bochner Integral.
1.3 Basic Function Spaces.
1.4 Functions of Bounded Variation.
1.5 Sobolev Spaces.
1.6 Unbounded Linear Operators.
1.7 Elements of Spectral Analysis.
1.8 Functional Calculus for Bounded Operators.
1.9 Functional Calculus for Unbounded Operators.
Chapter 2. Semigroups of Linear Operators
2.1 Uniformly Continuous Semigroups.
2.2 Generators of Uniformly Continuous Semigroups.
2.4 The Infinitesimal Generator.
Chapter 3. Generation Theorems
3.1 The Hille-Yosida Theorem. Necessity.
3.2 The Hille-Yosida Theorem. Sufficiency.
3.3 The Feller-Miyadera-Phillips Theorem.
3.4 The Lumer-Phillips Theorem.
3.5 Some Consequences.
3.7 The Dual of a C
3.8 The Sun Dual of a C
3.9 Stone Theorem.
Chapter 4. Differential Operators Generating C
4.1 The Laplace Operator with Dirichlet Boundary Conditions.
4.2 The Laplace Operator with Neumann Boundary Condition.
4.3 The Maxwell Operator.
4.4 The Directional Derivative.
4.5 The Schroedinger Operator.
4.6 The Wave Operator.
4.7 The Airy Operator.
4.8 The Equations of Linear Thermo