Singular Integrals, Rank One Perturbations and Clark Model in General Situation

DOI10.1007/978-3-319-51593-9_4zbMath1485.47016arXiv1506.00072OpenAlexW567669030MaRDI QIDQ4608792

Constanze Liaw, S. R. Treil'

Publication date: 28 March 2018

Published in: Association for Women in Mathematics Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.00072

zbMATH Keywords

regularizationHilbert transformsingular kernelsrank one perturbationsClark modelClark theoryabstract singular integral operators

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Hermitian and normal operators (spectral measures, functional calculus, etc.) (47B15) Perturbation theory of linear operators (47A55) Integral operators (47G10) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to operator theory (47-01) Operators arising in mathematical physics (47B93)

Related Items (5)

Miscellaneous on commutants mod normed ideals and quasicentral modulus. I ⋮ A controlled tangential Julia-Carathéodory theory via averaged Julia quotients ⋮ Elementary solutions for a model Boltzmann equation in one dimension and the connection to grossly determined solutions ⋮ Perspectives on general left-definite theory ⋮ Rank-one perturbations and Anderson-type Hamiltonians

Cites Work

• Clark model in the general situation
• Bochner-Pearson-type characterization of the free Meixner class
• Two-state free Brownian motions
• Coexistence of spectra in rank-one perturbation problems.
• Rank one perturbations and singular integral operators
• Dynamical localization for unitary Anderson models
• Absence of diffusion in the Anderson tight binding model for large disorder or low energy
• Localization at large disorder and at extreme energies: an elementary derivation
• Operators with singular continuous spectrum. II: Rank one operators
• Instability of dense point spectrum under finite rank perturbations
• Dynamical localization for \(d\)-dimensional random quantum walks
• Linear resolvent growth of rank one perturbation of a unitary operator does not imply its similarity to a normal operator.
• Regularizations of general singular integral operators
• Localization for random unitary operators
• Approach to the extended states conjecture
• Dynamical delocalization in random Landau Hamiltonians
• One dimensional perturbations of restricted shifts
• Harmonic analysis of operators on Hilbert space
• Cyclicity in rank-1 perturbation problems
• Delocalization for the 3D discrete random Schrödinger operator at weak disorder
• An Invitation to Random Schroedinger operators
• Singular continuous spectrum under rank one perturbations and localization for random hamiltonians
• Localization for Schrodinger operators with random vector potentials
• A geometric approach to finite rank unitary perturbations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Singular Integrals, Rank One Perturbations and Clark Model in General Situation