Asymptotics of the spectrum of nonsmooth perturbations of differential operators of order \(2m\)

DOI10.1134/S0001434611110216zbMath1281.47029MaRDI QIDQ2435878

E. F. Akhmerova

Publication date: 20 February 2014

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Hilbert spaceDirichlet boundary conditionsquasidifferential expressionperturbation of a differential operatorresolvent of an operatorspectrum of perturbations

Mathematics Subject Classification ID

Asymptotic distributions of eigenvalues in context of PDEs (35P20) Perturbation theory of linear operators (47A55) General theory of ordinary differential operators (47E05)

Related Items (8)

Sharp eigenvalue asymptotics of fourth-order differential operators ⋮ The matrix analysis of spectral projections for the perturbed self-adjoint operators ⋮ A one-dimensional Schrödinger operator with square-integrable potential ⋮ On the Hochstadt–Lieberman theorem for the fourth-order binomial operator ⋮ Spectral asymptotics and a trace formula for a fourth-order differential operator corresponding to thin film equation ⋮ Spectral analysis of an even order differential operator with square integrable potential ⋮ Spectral data asymptotics for the higher-order differential operators with distribution coefficients ⋮ Spectral properties of an even-order differential operator

Cites Work

• Unnamed Item
• Asymptotics of spectrum of a harmonic oscillator perturbed by a nonsmooth potential
• Spectral asymptotics for nonsmooth perturbations of differential operators and trace formulas
• Spectral asymptotics and trace formulas for differential operators with unbounded coefficients
• Asymptotics of eigenvalues and eigenfunctions and the trace formula for a potential that contains \(\delta\)-functions.
• Sturm-Liouville operators with singular potentials
• The eigenvalue and trace of the Sturm-Liouville operator as differentiable functions of a summable potential
• On the eigenvalues of the Sturm-Liouville operator with potentials from Sobolev spaces

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