Twisted spherical means in annular regions in C ⁿ and support theorems

2009/03/23 by Rama Rawat, Rawat, Rama, R. K. Srivastava +1
Mathematics · #43A85 #44A35 #53C65 #Analytic and geometric function theory #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical functions and polynomials #math.FA #msc:43A85 #msc:44A35 #msc:53C65

paper · pdf · doi:10.48550/arxiv.0903.3854

Published: Annales de l'institut Fourier, 59 no. 6 (2009), p. 2509-2523

openalex publication_date 2009/03/23 · arxiv created 2010/09/07 · arxiv updated 2010/09/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Let Z(Ann(r,R)) be the class of all continuous functions f on the annulus Ann(r,R) in \mathbb Cⁿ with twisted spherical mean f × μ_s(z)=0, whenever z∈ \mathbb Cⁿ and s >0 satisfy the condition that the sphere S_s(z)⊆ Ann(r, R) and ball B_r(0)⊆ B_s(z). In this paper, we give a characterization for functions in Z(Ann(r,R)) in terms of their spherical harmonic coefficients. We also prove support theorems for the twisted spherical means in \mathbb Cⁿ which improve some of the earlier results.

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