<電子ブック>
Stochastic Spectral Theory for Selfadjoint Feller Operators : A functional integration approach

責任表示
著者
本文言語
出版者
出版年
出版地
関連情報
概要 A beautiful interplay between probability theory (Markov processes, martingale theory) on the one hand and operator and spectral theory on the other yields a uniform treatment of several kinds of Hami...ltonians such as the Laplace operator, relativistic Hamiltonian, Laplace-Beltrami operator, and generators of Ornstein-Uhlenbeck processes. For such operators regular and singular perturbations of order zero and their spectral properties are investigated. A complete treatment of the Feynman-Kac formula is given. The theory is applied to such topics as compactness or trace class properties of differences of Feynman-Kac semigroups, preservation of absolutely continuous and/or essential spectra and completeness of scattering systems. The unified approach provides a new viewpoint of and a deeper insight into the subject. The book is aimed at advanced students and researchers in mathematical physics and mathematics with an interest in quantum physics, scattering theory, heat equation, operator theory, probability theory and spectral theory.続きを見る
目次 1 Basic Assumptions of Stochastic Spectral Analysis:Free Feller Operators
A Introduction
B Assumptions and Free Feller Generators
C Examples
D Heat kernels
E Summary of Schrödinger semigroup theory
2 Perturbations of Free Feller Operators
The framework of stochastic spectral analysis
A Regular perturbations
B Integral kernels, martingales, pinned measures
C Singular perturbations
3 Proof of Continuity and Symmetry of Feynman-Kac Kernels
4 Resolvent and Semigroup Differences for Feller Operators: Operator Norms
A Regular perturbations
B Singular perturbations
5 Hilbert-Schmidt Properties of Resolvent and Semigroup Differences
A Regular perturbations
B Singular perturbations
6 Trace Class Properties of Semigroup Differences
A General trace class criteria
B Regular perturbations
C Singular perturbations
7 Convergence of Resolvent Differences
8 Spectral Properties of Self-adjoint Feller Operators
A Qualitative spectral results
B Quantitative estimates for regular potentials
C Quantitative estimates for singular potentials in terms of the weighted Laplace transform of the occupation time (for large coupling parameters)
Appendix A Spectral Theory
Appendix B Semigroup Theory
Appendix C Markov Processes, Martingales and Stopping Times
Appendix D Dirichlet Kernels, Harmonic Measures, Capacities
Appendix E Dini's Lemma, Scheffé's Theorem, Monotone Class Theorem
References
Index of Symbols.
続きを見る
本文を見る Full text available from SpringerLink ebooks - Mathematics and Statistics (Archive)

詳細

レコードID
主題
SSID
eISBN
登録日 2020.06.27
更新日 2020.06.28

この資料を見た人はこんな資料も見ています