On Instability of the absolutely continuous spectrum of dissipative Schrödinger operators and Jacobi matrices

DOI10.1090/S1061-0022-06-00907-1zbMath1108.47015MaRDI QIDQ5481305

Roman Romanov

Publication date: 9 August 2006

Published in: St. Petersburg Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

Schrödinger operatordissipative operatorsabsolutely continuous subspace

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Perturbation theory of linear operators (47A55) Linear symmetric and selfadjoint operators (unbounded) (47B25) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Jacobi (tridiagonal) operators (matrices) and generalizations (47B36)

Cites Work

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrödinger operators
• On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
• Scattering and wave operators for one-dimensional Schrödinger operators with slowly decaying nonsmooth potentials.
• Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators
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