Asymptotic Distribution of Eigenvalues of Differential Operators

Inhaltsverzeichnis

• 1. The Weyl-Hörmander Calculus of Pseudodifferential Operators.
• §1. Classes of Symbols.
• §2. Estimates for Solutions of Schrödinger-Type Equations.
• §3. The Fundamental Theorems of Calculus.
• §4. Continuity of Pseudodifferential Operators.
• §5. Weight Spaces of Sobolev Type.
• §6. Action of Pseudodifferential Operators in Weight Spaces.
• 2. Basic Theorems of the Method of Approximate Spectral Projection for Scalar and Matrix Operators.
• §7. Formulation of the Basic Theorems.
• §8. Auxiliary Propositions.
• §9. Proof of Theorem 7.2 for the Scalar Case.
• §10. Proof of Theorem 7.3 for the Scalar Case.
• §11. Proofs of Theorems 7.2 and 7.3 for the Matrix Case.
• §12. Proofs of Theorems 7.1, 7.4, and 7.5.
• 3. Operators in a Bounded Domain.
• §13. Douglis-Nirenberg Elliptic Operators. Dirichlet-Type Problems.
• §14. General Boundary Value Problems for Elliptic Operators.
• §15. Problems with Resolvable Constraints.
• §16. Electromagnetic Resonator.
• §17. Asymptotics of the Discrete Spectrum of Douglis—Nirenberg Operators with a Totally Disconnected Essential Spectrum.
• §18. Linearized Stationary Navier—Stokes System.
• §19. Asymptotics for Eigenfrequencies of a Shell in a Vacuum.
• 4. Operators in Unbounded Domains.
• §20. Schrödinger Operators with Increasing Potential.
• §21. Asymptotics of a Discrete Spectrum of Schrödinger Operators and Dirac Operators with Decreasing Potentials.
• 5. Asymptotics of the Spectrum of Pseudodifferential Operators with Operator-Valued Symbols and Some Applications.
• §22. Pseudodifferential Operators with Operator-Valued Symbols.
• §23. Boundary Value Problems in Strongly Anisotropic Domains.
• 6. Degenerate Differential Operators.
• §24. General Analysis of Degenerate Operators and Generalizations of the Weyl Formula.
• §25. Schrödinger Operators with Degenerate Homogeneous Potential.
• §26. Model Problems for Degenerate Differential Operators in a Bounded Domain.
• §27. Degenerate Differential Operators in a Bounded Domain.
• §28. Degenerate Differential Operators in an Unbounded Domain.
• Appendix: Basic Variational Theorems.
• A Brief Review of the Bibliography.
• Notation Index.