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AuthorHislop, P. D. author
TitleIntroduction to Spectral Theory [electronic resource] : With Applications to Schrรถdinger Operators / by P. D. Hislop, I. M. Sigal
ImprintNew York, NY : Springer New York : Imprint: Springer, 1996
Connect tohttp://dx.doi.org/10.1007/978-1-4612-0741-2
Descript IX, 338 p. online resource

CONTENT

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: Weylโ{128}{153}s Criterion -- 8 Self-Adjointness: Part 1. The Kato Inequality -- 9 Compact Operators -- 10 Locally Compact Operators and Their Application to Schrรถdinger Operators -- 11 Semiclassical Analysis of Schrรถdinger Operators I: The Harmonic Approximation -- 12 Semiclassical Analysis of Schrรถdinger Operators II: The Splitting of Eigenvalues -- 13 Self-Adjointness: Part 2. The Kato-Rellich Theorem 131 -- 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 -- 18 Spectral Deformation of Schrรถdinger Operators -- 19 The General Theory of Spectral Stability -- 20 Theory of Quantum Resonances II: The Shape Resonance Model -- 21 Quantum Nontrapping Estimates -- 22 Theory of Quantum Resonances III: Resonance Width -- 23 Other Topics in the Theory of Quantum Resonances -- Appendix 1. Introduction to Banach Spaces -- A1.1 Linear Vector Spaces and Norms -- A1.2 Elementary Topology in Normed Vector Spaces -- A1.3 Banach Spaces -- A1.4 Compactness -- 1. Density results -- 2. The Hรถlder Inequality -- 3. The Minkowski Inequality -- 4. Lebesgue Dominated Convergence -- Appendix 3. Linear Operators on Banach Spaces -- A3.1 Linear Operators -- A3.2 Continuity and Boundedness of Linear Operators -- A3.3 The Graph of an Operator and Closure -- A3.4 Inverses of Linear Operators -- A3.5 Different Topologies on L(X) -- Appendix 4. The Fourier Transform, Sobolev Spaces, and Convolutions -- A4.1 Fourier Transform -- A4.2 Sobolev Spaces -- A4.3 Convolutions -- References


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