# On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators

@article{Gilbert1987OnSA, title={On subordinacy and analysis of the spectrum of one-dimensional Schr{\"o}dinger operators}, author={Daphne J. Gilbert and David B. Pearson}, journal={Journal of Mathematical Analysis and Applications}, year={1987}, volume={128}, pages={30-56} }

## 253 Citations

On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 1989

Synopsis The theory of subordinacy is extended to all one-dimensional Schrödinger operatorsfor which the corresponding differential expression L = – d2/(dr2) + V(r) is in the limit point case at both…

Modified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators

- Mathematics
- 1998

Abstract:Using control of the growth of the transfer matrices, wediscuss the spectral analysis of continuum and discrete half-line Schrödinger operators with slowly decaying potentials. Among our…

Eigenfunction Expansions Associated with the One-Dimensional Schrödinger Operator

- Mathematics
- 2013

We consider the form of eigenfunction expansions associated with the time-independent Schrodinger operator on the line, under the assumption that the limit point case holds at both of the infinite…

Finite Gap Potentials and WKB Asymptotics¶for One-Dimensional Schrödinger Operators

- Mathematics
- 2001

Abstract: Consider the Schrödinger operator H=−d2/dx2+V(x) with power-decaying potential V(x)=O(x−α). We prove that a previously obtained dimensional bound on exceptional sets of the WKB method is…

Absolutely continuous spectrum of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials

- Mathematics
- 1996

We prove that for any one-dimensional Schrödinger operator with potentialV(x) satisfying decay condition|V(x)|≦Cx−3/4−ε, the absolutely continuous spectrum fills the whole positive semi-axis. The…

Half-line Schrödinger operators with no bound states

- Mathematics
- 2003

acting in L2([0, c~)) with the boundary condition r For convenience, we require that the potential, V, be uniformly locally square integrable. We write l~(L 2) for the Banach space of such functions.…

Nontangential Limit of the Weyl m-Functions for the Ergodic Schrödinger Equation

- Mathematics
- 1998

This paper deals with the spectral and qualitative problems associated with the one-dimensional ergodic Schrödinger equation. Let A2 be the set of those energies for which the real projective flow…

α-Continuity Properties of One-Dimensional Quasicrystals

- Mathematics
- 1998

Abstract:
We apply the Jitomirskaya-Last extension of the Gilbert-Pearson theory to discrete one-dimensional Schrödinger operators with potentials arising from generalized Fibonacci sequences. We…

Bounds for the points of spectral concentration of one-dimensional schrodinger operators

- Mathematics
- 2004

We investigate the phenomenon of spectral concentration for one-dimensional Schrodinger operators with decaying potentials on the half-line. For suitable classes of short range and long range…

On subordinacy and spectral multiplicity for a class of singular differential operators

- MathematicsProceedings of the Royal Society of Edinburgh: Section A Mathematics
- 1998

The spectral multiplicity of self-adjoint operators H associated with singular differential expressions of the form is investigated. Based on earlier work of I. S. Kac and recent results on…

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