# Schr\"odinger operators on a half-line with inverse square potentials

@article{Kovak2014SchrodingerOO, title={Schr\"odinger operators on a half-line with inverse square potentials}, author={Hynek Kovař{\'i}k and Françoise Truc}, journal={arXiv: Mathematical Physics}, year={2014} }

We consider Schr\^odinger operators $H_\alpha$ given by equation (1.1) below. We study the asymptotic behavior of the spectral density $E(H_\alpha, \lambda)$ when $\lambda$ goes to $0$ and the $L^1\to L^\infty$ dispersive estimates associated to the evolution operator $e^{-i t H_\alpha}$. In particular we prove that for positive values of $\alpha$, the spectral density tends to zero as $\lambda\to 0$ with higher speed compared to the spectral density of Schr\"odinger operators with a short…

## 24 Citations

### On Schrödinger Operators with Inverse Square Potentials on the Half-Line

- Mathematics
- 2017

The paper is devoted to operators given formally by the expression $$\begin{aligned} -\partial _x^2+\left( \alpha -\frac{1}{4}\right) \frac{1}{x^{2}}. \end{aligned}$$-∂x2+α-141x2.This expression is…

### Improved time-decay for a class of scaling critical electromagnetic Schr\"odinger flows

- Mathematics
- 2015

### Remarks on endpoint Strichartz estimates for Schr\"odinger equations with the critical inverse-square potential

- Mathematics
- 2016

### Dispersion Estimates for Spherical Schr\"odinger Equations: The Effect of Boundary Conditions

- Mathematics, Physics
- 2016

We investigate the dependence of the $L^1\to L^\infty$ dispersive estimates for one-dimensional radial Schr\"o\-din\-ger operators on boundary conditions at $0$. In contrast to the case of additive…

### On Schrödinger Operators with Inverse Square Potentials on the Half-Line

- Materials ScienceAnnales Henri Poincaré
- 2016

The paper is devoted to operators given formally by the expression -∂x2+α-141x2.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

### Uniform resolvent and Strichartz estimates for Schr\"odinger equations with critical singularities

- Mathematics
- 2016

This paper deals with global dispersive properties of Schr\"odinger equations with real-valued potentials exhibiting critical singularities, where our class of potentials is more general than…

### The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes

- MathematicsLetters in Mathematical Physics
- 2017

In the setting of asymptotically anti-de Sitter spacetimes, we consider Klein–Gordon fields subject to Dirichlet boundary conditions, with mass satisfying the Breitenlohner–Freedman bound. We…

### On the Domains of Bessel Operators

- Art, MathematicsAnnales Henri Poincaré
- 2021

We consider the Schrödinger operator on the halfline with the potential (m2-14)1x2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

### Dispersion Estimates for Spherical Schr\"odinger Equations with Critical Angular Momentum

- Mathematics, Physics
- 2016

We derive a dispersion estimate for one-dimensional perturbed radial Schr\"odinger operators where the angular momentum takes the critical value $l=-\frac{1}{2}$. We also derive several new estimates…

### The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes

- Mathematics
- 2016

In the setting of asymptotically anti-de Sitter spacetimes, we consider Klein–Gordon fields subject to Dirichlet boundary conditions, with mass satisfying the Breitenlohner–Freedman bound. We…

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