Abstract
Let Z r,R be the class of all continuous functions f on the annulus Ann(r, R) in the real hyperbolic space \(\mathbb B^n\) with spherical means M s f(x) = 0, whenever s > 0 and \(x\in\mathbb B^n\) are such that the sphere S s (x) ⊂ Ann(r, R) and \(B_r(o)\subseteq B_s(x).\) In this article, we give a characterization for functions in Z r,R . In the case R = ∞, this result gives a new proof of Helgason’s support theorem for spherical means in the real hyperbolic spaces.
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RAWAT, R., SRIVASTAVA, R.K. Spherical means in annular regions in the n-dimensional real hyperbolic spaces. Proc Math Sci 121, 311–325 (2011). https://doi.org/10.1007/s12044-011-0037-4
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DOI: https://doi.org/10.1007/s12044-011-0037-4