Explicit fundamental solution for the operator L+α|T| on the Gelfand pair (ℍ_n,U(n))

2019/12/06 by Isolda Cardoso, Cardoso, Isolda E., Mauro Subils +3
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Waves and Solitons #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1912.04209

openalex publication_date 2019/12/06 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

By means of the spherical functions associated to the Gelfand pair (ℍ_n,U(n)) we define the operator L+α|T|, where L denotes the Heisenberg sublaplacian and T denotes de 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

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