Fractional Schrödinger equations with singular potentials of higher order. II: Hypoelliptic case

Abstract

In this paper we consider the space-fractional Schrödinger equation with a singular potential for a wide class of fractional hypoelliptic operators. Such analysis can be conveniently realised in the setting of graded Lie groups. The paper is a continuation and extension of a previous one where the classical Schrödinger equation on ${\mathbb{R}}^n$ with singular potentials was considered.

arXiv commentThis work is a continuation and an extension of the previous one, see arXiv:2004.10182v2, on ${\mathbb{R}}^n$. arXiv admin note: substantial text overlap with arXiv:2105.12862

References in corpus (6)

• Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
• Hyperbolic second order equations with non-regular time dependent coefficients
• Wave equation for operators with discrete spectrum and irregular propagation speed
• Fractional Klein-Gordon equation with singular mass
• The heat equation with strongly singular potentials
• Fractional Klein-Gordon equation with singular mass. II: Hypoelliptic case