Fractional SchrÖdinger Equations with Singular Potentials of Higher Order. II: Hypoelliptic Case

Chatzakou M. Ruzhansky M. Tokmagambetov N.
February 2022 Elsevier Ltd

Reports on Mathematical Physics
2022 #89 Issue 1 59 - 79 pp.

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 [2] where the classical Schrödinger equation on Rⁿ with singular potentials was considered.

distributional coefficient , generalised solution , graded Lie group , regularisation , Rockland operator , Schrödinger equation , singular potential , very weak solution

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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, 281 Krijgslaan, Ghent, S8 9000, Belgium
School of Mathematical Sciences, Queen Mary University of London, Mile End Rd, Stepney, London, El 4NS, United Kingdom
Institute of Mathematics and Mathematical Modeling, 125 Pushkin str., Almaty, 050010, Kazakhstan
Al-Farabi Kazakh National University, 71 Al-Farabi ave., Almaty, 050040, Kazakhstan

Department of Mathematics: Analysis
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modeling
Al-Farabi Kazakh National University

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