Dispersion Estimates for One-Dimensional Schrödinger Equations with Singular Potentials

Abstract

We derive a dispersion estimate for one-dimensional perturbed radial Schrödinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near the edge of the continuous spectrum.

26 pages

References in corpus (7)

• Dispersive estimates for Schrodinger operators in dimensions one and three
• On the Singular Weyl-Titchmarsh Function of Perturbed Spherical Schroedinger Operators
• Dispersion Estimates for One-dimensional Discrete Schrödinger and Wave Equations
• Inverse Eigenvalue Problems for Perturbed Spherical Schroedinger Operators
• Time decay of scaling invariant Schroedinger equations on the plane
• Spectral asymptotics for canonical systems
• The O(n) ${\varphi }^4$ model with free surfaces in the large-$n$ limit: Some exact results for boundary critical behaviour, fluctuation-induced forces and distant-wall corrections

Cited by in corpus (6)

• On Schroedinger operators with inverse square potentials on the half-line
• Jacobi Polynomials, Bernstein-type Inequalities and Dispersion Estimates for the Discrete Laguerre Operator
• A transmutation operator method for solving the inverse quantum scattering problem
• Transformation operators for spherical Schrödinger operators
• $L^p-L^{p^{\prime }}$ estimates for matrix Schrödinger equations
• Dispersion Estimates for Spherical Schrödinger Equations with Critical Angular Momentum