Asymptotic Distribution of Eigenvalues of Differential Operators: Mathematics and its Applications, cartea 53

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.