Spectral and scattering theory for differential and Hankel operators

DOI10.1016/j.aim.2016.12.032zbMath1360.34172arXiv1511.04683OpenAlexW2963658189MaRDI QIDQ507223

Dimitri Yafaev

Publication date: 3 February 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1511.04683

zbMATH Keywords

Mellin transformabsolutely continuous spectrumasymptotic behavior of eigenfunctionsdegeneracy of coefficients at infinitydifferential operators of arbitrary ordergeneralized Carleman operators

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) General spectral theory of ordinary differential operators (34L05) Linear symmetric and selfadjoint operators (unbounded) (47B25) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) General theory of ordinary differential operators (47E05) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Scattering theory of linear operators (47A40) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items

Universal relations in asymptotic formulas for orthogonal polynomials ⋮ A new representation of Hankel operators and its spectral consequences

Cites Work

• A commutator method for the diagonalization of Hankel operators
• Absence of singular continuous spectrum for certain self-adjoint operators
• The scattering amplitude for the Schrödinger equation with a long-range potential
• Quasi-diagonalization of Hankel operators
• The inverse spectral problem for selfadjoint Hankel operators
• Quasi-Carleman operators and their spectral properties
• Criteria for Hankel operators to be sign-definite
• Spectral and scattering theory for perturbations of the Carleman operator
• On the Hilbert Matrix, I
• On Krein’s example
• Spectral and scattering theory of fourth order differential operators
• Diagonalizations of two classes of unbounded Hankel operators
• Properties of the 𝑆-matrix of the one-dimensional Schrödinger equation
• On the Nature of the Spectrum of Singular Second Order Linear Differential Equations
• \(C_0\)-groups, commutator methods and spectral theory of \(N\)-body Hamiltonians
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