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Fractional Klein-Gordon equation with singular mass. II: Hypoelliptic case
(Taylor & Francis, 2021-07)
In this paper we consider a fractional wave equation for hypoelliptic operators with a singular mass term depending on the spacial variable and prove that it has a very weak solution. Such analysis can be conveniently ...
Fractional Schrödinger equations with singular potentials of higher order. II: Hypoelliptic case
(Elsevier, 2021)
In this paper we consider the space-fractional Schr\"odinger 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 ...
On a class of anharmonic oscillators
(Elsevier, 2021)
In this work we study a class of anharmonic oscillators within the framework of the Weyl-H\"ormander calculus. The anharmonic oscillators arise from several applications in mathematical physics as natural extensions of the ...
Anisotropic Shannon inequality
(2021-06-27)
In this note we prove the anisotropic version of the Shannon inequality. This can be conveniently realised in the setting of Folland and Stein's homogeneous groups. We give two proofs: one giving the best constant, and ...
The heat equation with singular potentials. II: Hypoelliptic case
In this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded ...