A Reconstruction Theorem for Riemannian Symmetric Spaces of Noncompact Type |
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Authors: | Matthew B Stenzel |
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Institution: | (1) Department of Mathematics, Auburn University, Auburn, AL 36849, USA;(2) Department of Mathematics, Nankai University, Tianjin, China |
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Abstract: | Let f be a rapidly decreasing radial function on a Riemannian symmetric space of noncompact type whose spherical Fourier transform
has compact support. We prove a reconstruction theorem which recovers f from the values of an integral operator applied to f on a discrete subset. When G/K is of the complex type we prove a sampling formula recovering f from its own values on a discrete subset. We give explicit results for three dimensional hyperbolic space. |
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