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

  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},
  • D. Gilbert, D. Pearson
  • Published 15 November 1987
  • Mathematics
  • Journal of Mathematical Analysis and Applications
On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints
  • D. Gilbert
  • Mathematics
    Proceedings 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
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
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
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
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
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
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
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
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
  • D. Gilbert
  • Mathematics
    Proceedings 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


VII.—On the Spectrum of Ordinary Second Order Differential Operators.
  • J. ChaudhuriW. N. Everitt
  • Mathematics
    Proceedings of the Royal Society of Edinburgh. Section A. Mathematical and Physical Sciences
  • 1969
Synopsis This paper considers properties of the spectrum of differential operators derived from differential expressions of the second order. The object is to link the spectral properties of these
On the Smallness of Isolated Eigenfunctions
which is satisfied by x yj(t) at t = 0). According to Weyl [3], p. 238, the assumption (2) precludes the existence of a A0 corresponding to which (3) had two linearly independent solutions of class
Real and complex analysis
Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures
Monotone Matrix Functions and Analytic Continuation
I. Preliminaries.- II. Pick Functions.- III. Pick Matrices and Loewner Determinants.- IV. Fatou Theorems.- V. The Spectral Theorem.- VI. One-Dimensional Perturbations.- VII. Monotone Matrix
Ordinary Differential Equations
Foreword to the Classics Edition Preface to the First Edition Preface to the Second Edition Errata I: Preliminaries II: Existence III: Differential In qualities and Uniqueness IV: Linear Differential
Real And Abstract Analysis
The first € price and the £ and $ price are net prices, subject to local VAT, and the €(D) includes 7% for Germany, the€(A) includes 10% for Austria.
Quantum Mechanics