Real analyticity of solutions to Schr\"odinger equations involving fractional Laplacians

TL;DR

This paper proves that solutions to certain nonlocal Schrödinger equations with analytic potentials are themselves analytic across all dimensions.

Contribution

It establishes the real analyticity of solutions to nonlocal linear Schrödinger equations involving fractional Laplacians, extending understanding of their regularity.

Findings

Solutions are analytic in  for specified equations.

Analyticity holds for equations with analytic potentials.

Results apply across all dimensions   1.

Abstract

We prove analyticity of solutions in $\mathbb{R}^{n}$, $n\ge1$, to certain nonlocal linear Schr\"odinger equations with analytic potentials.