Spectral Theory of Random Schrödinger Operators: Probability and Its Applications
Autor R. Carmona, J. Lacroixen Limba Engleză Hardback – 1990
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Birkhäuser Boston – 1990 | 914.41 lei 6-8 săpt. |
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Specificații
ISBN-13: 9780817634865
ISBN-10: 081763486X
Pagini: 589
Ilustrații: XXVI, 589 p.
Dimensiuni: 155 x 235 x 33 mm
Greutate: 1.04 kg
Ediția:1990
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria Probability and Its Applications
Locul publicării:Boston, MA, United States
ISBN-10: 081763486X
Pagini: 589
Ilustrații: XXVI, 589 p.
Dimensiuni: 155 x 235 x 33 mm
Greutate: 1.04 kg
Ediția:1990
Editura: Birkhäuser Boston
Colecția Birkhäuser
Seria Probability and Its Applications
Locul publicării:Boston, MA, United States
Public țintă
ResearchCuprins
I Spectral Theory of Self-Adjoint Operators.- 1 Domains, Adjoints, Resolvents and Spectra.- 2 Resolutions of the Identity.- 3 Representation Theorems.- 4 The Spectral Theorem.- 5 Quadratic Forms and Self-adjoint Operators.- 6 Self-adjoint Extensions of Symmetric Operators.- 7 Problems.- 8 Notes and Complements.- II Schrödinger Operators.- 1 The Free Hamiltonians.- 2 Schrödinger Operators as Perturbations.- 3 Path Integral Formulas.- 4 Eigenfunctions.- 5 Problems.- 6 Notes and Complements.- III One-Dimensional Schrödinger Operators.- 1 The Continuous Case.- 2 The Lattice Case.- 3 Approximations of the Spectral Measures.- 4 Spectral Types.- 5 Quasi-one Dimensional Schrödinger Operators.- 6 Problems.- 7 Notes and Complements.- IV Products of Random Matrices.- 1 General Ergodic Theorems.- 2 Matrix Valued Systems.- 3 Group Action on Compact Spaces.- 4 Products of Independent Random Matrices.- 5 Markovian Multiplicative Systems.- 6 Boundaries of the Symplectic Group.- 7 Problems.- 8 Notes and Comments.- V Ergodic Families of Self-Adjoint Operators.- 1 Measurability Concepts.- 2 Spectra of Ergodic Families.- 3 The Case of Random Schrödinger Operators.- 4 Regularity Properties of the Lyapunov Exponents.- 5 Problems.- 6 Notes and Complements.- VI The Integrated Density of States.- 1 Existence Problems.- 2 Asymptotic Behavior and Lifschitz Tails.- 3 More on the Lattice Case.- 4 The One Dimensional Cases.- 5 Problems.- 6 Notes and Complements.- VII Absolutely Continuous Spectrum and Inverse Theory.- 1 The w-function.- 2 Periodic and Almost Periodic Potentials.- 3 The Absolutely Continuous Spectrum.- 4 Inverse Spectral Theory.- 5 Miscellaneous.- 6 Problems.- 7 Notes and Complements.- VIII Localization in One Dimension.- 1 Pointwise Theory.- 2 Perturbation Theory.- 3 OperatorTheory.- 4 Localization for Singular Potentials.- 5 Non-Stationary Processes.- 6 Problems.- 7 Notes and Complements.- IX Localization in Any Dimension.- 1 Exponential Decay of the Green’s Function at Fixed Energy.- 2 Localization for A.C. Potentials.- 3 A Direct Proof of Localization.- 4 Problems.- 5 Notes and Complements.- Notation Index.