Spectral properties of a class of reflectionless Schrödinger operators

DOI10.1016/j.jfa.2006.08.006zbMath1387.34120arXivmath/0603103OpenAlexW2084642318MaRDI QIDQ859628

Friedrich Gesztesy, Peter Yuditskii

Publication date: 16 January 2007

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0603103

zbMATH Keywords

spectral propertieshomogeneous setsreflectionless Schrödinger operators

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Spectrum, resolvent (47A10) General theory of ordinary differential operators (47E05)

Related Items

The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous, Homogeneity of the spectrum for quasi-periodic Schrödinger operators, Reflectionless Herglotz functions and Jacobi matrices, Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators, Some examples of generalized reflectionless Schrödinger potentials, Remarks on the generalized reflectionless Schrödinger potentials, Exponential upper bounds on the spectral gaps and homogeneous spectrum for the non-critical extended Harper's model, Stability of the non-critical spectral properties i: arithmetic absolute continuity of the integrated density of states, The absolutely continuous spectrum of Jacobi matrices, Szegő's theorem on Parreau-Widom sets, Mini-workshop: Reflectionless operators: the Deift and Simon conjectures. Abstracts from the mini-workshop held October 22--28, 2017, SOME REMARKS CONCERNING REFLECTIONLESS STURM–LIOUVILLE POTENTIALS, Reflectionless discrete Schrödinger operators are spectrally atypical, Direct Cauchy theorem and Fourier integral in Widom domains, Essential closures and AC spectra for reflectionless CMV, Jacobi, and Schrödinger operators revisited, Dynamics in the Szeő class and polynomial asymptotics, Equality of the spectral and dynamical definitions of reflection, On the Camassa-Holm and K-dV hierarchies, Right limits and reflectionless measures for CMV matrices, Limit-periodic Dirac operators with thin spectra, Counterexamples to the Kotani-Last conjecture for continuum Schrödinger operators via character-automorphic Hardy spaces

Cites Work

• On a theorem of Kac and Gilbert
• Hardy classes on infinitely connected Riemann surfaces
• On isospectral sets of Jacobi operators
• The recurrent Hill's equation
• Critical points of Green's function, harmonic measure, and the corona problem
• Sturm-Liouville operators and applications. Transl. from the Russian by A. Iacob
• Inverse spectral problem for limit-periodic Schrödinger operators
• Almost periodicity of some random potentials
• On a Sato-Segal-Wilson solutions of the K-dV equation
• On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
• An example of a Schrödinger equation with almost periodic potential and nowhere dense spectrum
• Almost periodic Schrödinger operators. I: Limit periodic potentials
• The rotation number for almost periodic potentials
• Almost periodic Jacobi matrices with homogeneous spectrum, infinite dimensional Jacobi inversion, and Hardy spaces of character-automorphic functions
• A complete spectral characterization of the double commutation method
• The \(\xi\) function
• Asymptotic behavior of polynomials orthonormal on a homogeneous set
• Borg-type theorems for matrix-valued Schrödinger operators
• The trace formula for Schrödinger operators on the line
• Espaces de Hardy et domains de Denjoy. (Hardy spaces and Denjoy domains)
• Almost periodic Sturm-Liouville operators with Cantor homogeneous spectrum
• Almost periodic Schrödinger operators. III: The absolutely continuous spectrum in one dimension
• On exponential representation of analytic functions in the upper half- plane with positive imaginary part
• A supplement to the paper on exponential representations of analytic functions in the upper half-plane with positive imaginary part
• The maximum principle for multiple-valued analytic functions
• \({\mathcal H}^p\) sections of vector bundles over Riemann surfaces
• Differential equations with non oscillatory eigenfunctions
• Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung
• On the Trace Approach to the Inverse Scattering Problem in Dimension One
• Weyl-Titchmarsh M -Function Asymptotics for Matrix-valued Schrödinger Operators
• On the determination of a differential equation from its spectral function
• APPROXIMATION OF INFINITE-ZONE POTENTIALS BY FINITE-ZONE POTENTIALS
• ON THE CLOSURE OF THE SET OF FINITE-ZONE POTENTIALS
• On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints
• On subordinacy and spectral multiplicity for a class of singular differential operators
• A generalisation of the inverse spectral theorem of Levitan and Gasymov
• ALMOST PERIODICITY OF INFINITE-ZONE POTENTIALS
• 𝑅-functions—analytic functions mapping the upper halfplane into itself
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• On Povzner–Wienholtz-type self-adjointness results for matrix-valued Sturm–Liouville operators
• 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
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item