On Schrödinger operators perturbed by fractal potentials

DOI10.1016/S0034-4877(00)80001-4zbMath0960.47001OpenAlexW2014328351MaRDI QIDQ1580726

Volodymyr Koshmanenko, Sergio A. Albeverio

Publication date: 14 May 2001

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(00)80001-4

zbMATH Keywords

Schrödinger operatorssingular perturbationsessential spectrumFriedrichs extensionnegative eigenvaluesself-similar fractalself-adjoint realizationlower semi-bounded

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Spectrum, resolvent (47A10) Perturbation theory of linear operators (47A55) Dilations, extensions, compressions of linear operators (47A20) Fractals (28A80)

Related Items (5)

Eigenvalues of singular measures and Connes' noncommutative integration ⋮ Weakly coupled bound state of 2-D Schrödinger operator with potential-measure ⋮ The rigged Hilbert spaces approach in singular perturbation theory ⋮ On negative eigenvalues of generalized Laplace operators. ⋮ Parametrization of supersingular perturbations in the method of rigged Hilbert spaces

Cites Work

• Some properties of Laplacians on fractals
• Schrödinger operators with singular interactions
• Schrödinger operator perturbed by operators related to null sets
• Singular rank one perturbations of self-adjoint operators and Krein theory of self-adjoint extensions
• On extension theory in \(L^ 2\)-spaces
• On form-sum approximations of singularly perturbed positive self-adjoint operators
• Singular perturbations of finite rank. Point spectrum
• On the Right Hamiltonian for Singular Perturbations: General Theory
• ON THE PROBLEM OF THE RIGHT HAMILTONIAN UNDER SINGULAR FORM-SUM PERTURBATIONS
• Square Powers of Singularly Perturbed Operators
• Perturbations of self-adjoint operators by singular bilinear forms
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