Fractional Schrödinger equations with singular potentials of higher order. II: Hypoelliptic case. (English) Zbl 07505716
Summary: 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 the first part [A. Altybay et al., Rep. Math. Phys. 87, No. 1, 129–144 (2021; Zbl 1527.35363)] where the classical Schrödinger equation on R\(^n\) with singular potentials was considered.
Keywords:
Schrödinger equation; generalised solution; singular potential; regularisation; rockland operator; distributional coefficient; very weak solution; graded Lie groupCitations:
Zbl 1527.35363References:
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