Introduction to spectral theory: with applications to Schrödinger operators/
P.D. Hislop and I.M. Sigal
- New York: Springer, 1996.
- ix, 337 p. : ill. ; 25 cm.
- (Applied mathematical sciences) v. 113 .
1. The Spectrum of Linear Operators and Hilbert Spaces -- 2. The Geometry of a Hilbert Space and Its Subspaces -- 3. Exponential Decay of Eigenfunctions -- 4. Operators on Hilbert Spaces -- 5. Self-Adjoint Operators -- 6. Riesz Projections and Isolated Points of the Spectrum -- 7. The Essential Spectrum: Weyl's Criterion -- 8. Self-Adjointness: Part 1. The Kato Inequality -- 9. Compact Operators -- 10. Locally Compact Operators and Their Application to Schrodinger Operators -- 11. Semiclassical Analysis of Schrodinger Operators I: The Harmonic Approximation -- 12. Semiclassical Analysis of Schrodinger Operators II: The Splitting of Eigenvalues -- 13. Self-Adjointness: Part 2. The Kato -- Rellich Theorem -- 14. Relatively Compact Operators and the Weyl Theorem -- 15. Perturbation Theory: Relatively Bounded Perturbations -- 16. Theory of Quantum Resonances I: The Aguilar-Balslev-Combes-Simon Theorem -- 17. Spectral Deformation Theory.