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Operator Methods in Mathematical Physics

Part of the Operator Theory: Advances and Applications Book Series (volume 227)

Editors: Janas, Jan; Kurasov, Pavel; Laptev, Ari; Naboko, Sergei

DOI: 10.1007/978-3-0348-0531-5

ISBN: 978-3-0348-0530-8

Publisher: Springer Basel - Springer Journals

Dec 12, 2012

1 - 10 of 10 Chapters

LitStream

Chapter 1Inverse Scattering for Non-classical Impedance Schrödinger Operators

Albeverio, Sergio; Hryniv, Rostyslav O.; Mykytyuk, Yaroslav V.; Perry, Peter A.

Pages: 1 –42

[We review recent progress in the direct and inverse scattering theory for one-dimensional Schrödinger operators in impedance form. Two classes of non-smooth impedance functions are considered. Absolutely continuous impedances correspond to singular Miura potentials that are distributions from...
LitStream

Chapter 2Finite and Infinite Gap Jacobi Matrices

Christiansen, Jacob S.

Pages: 43 –55

[The present paper reviews the theory of bounded Jacobi matrices whose essential spectrum is a finite gap set, and it explains how the theory can be extended to also cover a large number of infinite gap sets. Two of the central results are generalizations of Denisov–Rakhmanov’s theorem and...
LitStream

Chapter 3Derivation of Ginzburg-Landau Theory for a One-dimensional System with Contact Interaction

Frank, Rupert L.; Hainzl, Christian; Seiringer, Robert; Solovej, Jan Philip

Pages: 57 –88

[In a recent paper [7] we give the first rigorous derivation of the celebrated Ginzburg-Landau (GL)the ory, starting from the microscopic Bardeen- Cooper-Schrieffer (BCS)mo del. Here we present our results in the simplified case of a one-dimensional system of particles interacting via a...
LitStream

Chapter 4Eigenfunction Expansions Associated with the One-dimensional Schrödinger Operator

Gilbert, Daphne J.

Pages: 89 –105

[We consider the form of eigenfunction expansions associated with the time-independent Schrödinger operator on the line, under the assumption that the limit point case holds at both of the infinite endpoints. It is well known that in this situation the multiplicity of the operator may be one or...
LitStream

Chapter 5Spectral Minimal Partitions for a Thin Strip on a Cylinder or a Thin Annulus like Domain with Neumann Condition

Helffer, Bernard; Hoffmann-Ostenhof, Thomas

Pages: 107 –115

[We analyze “Neumann” spectral minimal partitions for a thin strip on a cylinder or for the thin annulus.]
LitStream

Chapter 6Jacobi and CMV Matrices with Coefficients of Generalized Bounded Variation

Lukic, Milivoje

Pages: 117 –121

[We consider Jacobi and CMV matrices with coefficients satisfying an \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}...
LitStream

Chapter 7Order Convergence Ergodic Theorems in Rearrangement Invariant Spaces

Muratov, Mustafa; Pashkova, Julia; Rubshtein, Ben-Zion

Pages: 123 –142

[We find necessary and sufficient conditions for order convergence of Cesáro averages of positive absolute contractions in rearrangement invariant spaces. We study the case, when the considered measure is infinite. The investigation of order convergence includes both Dominated and Individual...
LitStream

Chapter 8Local Approximation of Observables and Commutator Bounds

Nachtergaele, Bruno; Scholz, Volkher B.; Werner, Reinhard F.

Pages: 143 –149

[We discuss conditional expectations that can be used as generalizations of the partial trace for quantum systems with an infinite-dimensional Hilbert space of states.]
LitStream

Chapter 9The Spectra of Selfadjoint Extensions of Entire Operators with Deficiency Indices (1,1)

Silva, Luis O.; Toloza, Julio H.

Pages: 151 –164

[We give necessary and sufficient conditions for real sequences to be the spectra of selfadjoint extensions of an entire operator whose domain may be non-dense. For this spectral characterization we use de Branges space techniques and a generalization of Krein’s functional model for simple,...
LitStream

Chapter 10Asymptotics of Eigenvalues of an Energy Operator in a Problem of Quantum Physics

Yanovich, Eduard A.

Pages: 165 –177

[In this paper we consider eigenvalues asymptotics of the energy operator in one of the most interesting models of quantum physics, describing an interaction between two-level system and harmonic oscillator. The energy operator in this model can be reduced to a class of infinite Jacobi matrices....

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