Functional Calculus of Pseudodifferential Boundary Problems

Cover
Title page
Preface
Introduction
Chapter 1. Standard pseudodifferential boundary problems and their realizations
1.1. Introductory remarks
1.2. The calculus of pseudodifferential boundary problems
1.3. Green's formula
1.4. Realizations and normal boundary conditions
1.5. Parameter-ellipticity and parabolicity
1.6. Adjoints
1.7. Semiboundedness and coerciveness
Chapter 2. The calculus of parameter-dependent operators
2.1. Parameter-dependent pseudodifferential operators
2.2. The transmission condition
2.3. Parameter-dependent boundary symbols
2.4. Operators and kernels
2.5. Continuity, auxiliary operators
2.6. Composition of boundary symbol operators
2.7. Compositions in general
2.8. Extension of mapping properties, negative class
2.9. Strictly homogeneous symbols
Chapter 3. Parametrix and resolvent constructions
3.1. Ellipticity. Auxiliary reductions
3.2. The parametrix construction
3.3. The resolvent of a realization
3.4. Other special cases
Chapter 4. Some applications
4.1. Evolution problems
4.2. The heat operator
4.3. An index formula
4.4. Complex powers
4.5. Spectral asymptotics
4.6. Implicit eigenvalue problems
4.7. Singular perturbations
Appendix. Various prerequisites
A.1. General notation
A.2. Functions and distributions
A.3. Sobolev spaces
A.4. Spaces over subsets of IRn
A.5. Spaces over admissible manifolds
A.6. Notions from spectral theory
Bibliography
Index