Bounded solutions and absolute continuity of Sturm-Liouville operators

DOI10.1016/0022-247X(92)90112-QzbMath0785.34052MaRDI QIDQ1206893

Günter Stolz

Publication date: 1 April 1993

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

asymptotic propertiesSturm-Liouville equationabsolute continuity of the spectrum

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) General spectral theory of ordinary differential operators (34L05) General theory of ordinary differential operators (47E05) Growth and boundedness of solutions to ordinary differential equations (34C11)

Related Items (39)

Spectral theory for slowly oscillating potentials. I: Jacobi matrices ⋮ Operators with singular continuous spectrum. II: Rank one operators ⋮ Spectral concentration and rapidly decaying potentials ⋮ Stokes' phenomenon and the absolutely continuous spectrum of one-dimensional Schrödinger operators ⋮ The asymptotic nature of spectral functions in Sturm-Liouville problems with continuous spectrum ⋮ Spectral concentration and perturbed discrete spectra ⋮ Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials ⋮ Absolutely continuous spectrum for CMV matrices with small quasi-periodic Verblunsky coefficients ⋮ Schrödinger operators with dynamically defined potentials ⋮ Dirac operators with operator data of Wigner-von Neumann type ⋮ Schrödinger operators with slowly decaying Wigner-von Neumann type potentials ⋮ A class of Schrödinger operators with decaying oscillatory potentials ⋮ Stability of the absolutely continuous spectrum of the Schrödinger equation under slowly decaying perturbations and a. e. convergence of integral operators ⋮ Spectral analysis of the half-line Kronig-Penney model with Wigner-von Neumann perturbations ⋮ Solutions, spectrum, and dynamics for Schrödinger operators on infinite domains ⋮ The asymptotic form of the spectral function in Sturm–Liouville problems with a large potential like −x^c(c ≦ 2) ⋮ On the first trace formula for Schrödinger operators ⋮ Continuum eigenmodes in some linear stellar models ⋮ WKB asymptotic behavior of almost all generalized eigenfunctions for one-dimensional Schrödinger operators with slowly decaying potentials ⋮ On subordinacy and spectral multiplicity for a class of singular differential operators ⋮ Half-line Schrödinger operators with no bound states ⋮ On the application of some of M. G. Krein's results to the spectral analysis of Sturm-Liouville operators ⋮ Absolutely continuous spectrum of perturbed Stark operators ⋮ Absolutely continuous spectrum of discrete Schrödinger operators with slowly oscillating potentials ⋮ Low energy properties of the random displacement model ⋮ Modified Prüfer and EFGP transforms and deterministic models with dense point spectrum ⋮ Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators ⋮ Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators ⋮ On the location of spectral concentration for Sturm–Liouville problems with rapidly decaying potential ⋮ Wigner-von Neumann type perturbations of periodic Schrödinger operators ⋮ Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results ⋮ Uniqueness of solutions of the KdV-hierarchy via Dubrovin-type flows ⋮ Absolute continuity and spectral concentration for slowly decaying potentials ⋮ Schrödinger operators with few bound states ⋮ Schrödinger operators with decaying potentials: some counterexamples ⋮ Localization for one-dimensional, continuum, Bernoulli-Anderson models. ⋮ Revisiting the Christ–Kiselev’s multi-linear operator technique and its applications to Schrödinger operators ⋮ On the location of spectral concentration for perturbed discrete spectra ⋮ Embedded singular continuous spectrum for one-dimensional Schrödinger operators

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