Spectral and scattering theory for second order partial differential operators. (2017)

• Record Type: Book
• Further Information: Note: Kiyoshi Mochizuki.
• Authors: Mochizuki, Kiyoshi
• Contents: Cover; Title Page; Copyright Page; Dedication; Table of Contents; Preface; Introduction; 1: Second-Order Elliptic Operators in Exterior Domain; 1.1 Self-adjoint realization of the operator -- ∆a, b; 1.2 Short-range perturbations of -- ∆a, b; 1.3 Cases of more general potentials; 1.4 Operators with strongly singular potentials; 1.5 Notes and remarks; 2: Essential Spectrum of Self-Adjoint Operators; 2.1 Stability of the essential spectrum; 2.2 Essential spectrum of operators with exploding potentials; 2.3 Notes and remarks; 3: Statinary Equations and Functional Identities 3.1 Approximate phase for stationary equations3.2 Assumptions and examples of electric potentials; 3.3 Functional identities for stationary problems; 3.4 Notes and remarks; 4: Growth Properties of Generalized Eigenfunctions; 4.1 Statements of the theorems; 4.2 Proof of Theorem 4.1 when (K3.4)1 is required; 4.3 Proof of Theorem 4.1 when (K3.4)2 is required; 4.4 Notes and remarks; 5: Principle of Limiting Absorption and Absolute Continuity; 5.1 Radiation condition and unique existence of solutions; 5.2 Absolute continuity of the continuous spectrum 5.3 A modification of the radiation conditions5.4 Notes and remarks; 6: Spectral Representations and Scattering for Short-Range Pertubations; 6.1 Fourier inversion formula and the Laplace operator in Rn; 6.2 The case of short-range perturbations of the Laplace operator; 6.3 Stationary approach to the scattering theory; 6.4 An inverse scattering problem; 6.5 Notes and remarks; 7: Spectral Representations and Scattering 2, "Long-Range" Perturbations; 7.1 Spectral representation of the operator L; 7.2 Unitarity of F± and expression of F∗± 7.3 Time dependent representations for the stationary wave operators7.4 Proof of Propositions 7.4 and 7.5; 7.5 Notes and remarks; 8: One Dimensional Schrödinger Operators; 8.1 Schrödinger operators on a star graph; 8.2 Expression of the resolvent kernel and spectral representations; 8.3 Stationary approach to the Møller scattering theory; 8.4 Marchenko equation and inverse scattering; 8.5 Notes and remarks; 9: Uniform Resolvent Estimates and Smoothing Properties; 9.1 Magnetic Schrödinger operators in exterior domain; 9.2 Laplace operator and its perturbations in R2 9.3 Smoothing properties for Schrödinger evolution equations9.4 Smoothing properties for relativistic Schrödinger equations; 9.5 Notes and remarks; 10: Scattering for Time Dependent Perturbations; 10.1 Abstract setting for time dependent small perturbations; 10.2 Applications to Schrödinger, Klein-Gordon, and wave equations; 10.3 Space-time weighted energy methods for wave equations; 10.4 Decay-nondecay problems for time dependent complex potential; 10.5 Inverse scattering for small nonself-adjoint perturbation of wave equations; 10.6 Notes and remarks
• Publisher Details: Boca Raton, FL : CRC Press
• Publication Date: 2017
• Extent: 1 online resource
• Subjects: 515/.7222; MATHEMATICS / Functional Analysis; Spectral theory (Mathematics); Differential equations; MATHEMATICS / Calculus; MATHEMATICS / Mathematical Analysis; MATHEMATICS / Arithmetic; Electronic books
• Languages: English
• ISBNs: 9781351648943; 1351648942
• Related ISBNs: 9781498756020
• Notes: Note: Online resource; title from PDF title page (EBSCO, viewed June 12, 2017).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.