Explicit fundamental solution for the operator $$L+\alpha |T|$$ on the Gelfand pair $$(\mathbb {H}_{n},U(n))$$.

CARDOSO, I. E.; SUBILS, M.; VIDAL, R. E.

Journal of Pseudo-Differential Operators and Applications

Springer

Año: 2021 vol. 12

1662-9981

By means of the spherical functions associated to the Gelfand pair (Hn,U(n)) we define the operator L+α|T|, where L denotes the Heisenberg sublaplacian and T denotes the central element of the Heisenberg Lie algebra, we establish a notion of fundamental solution and explicitly compute in terms of the Gauss hypergeometric function. For α