Spherical Spectral Analysis on Subsets of Compact Symmetric Spaces
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This chapter is devoted to so-called “freak theorems” and their local analogues. Results due to Radon, Ungar, Schneider, Berenstein, and Zalcman are described. These results are extended to convolution equations on arbitrary compact symmetric spaces. For compact symmetric spaces of rank one, local analogues of “freak theorems” are obtained. It is shown that all the assumptions in these results cannot be relaxed.
KeywordsSymmetric Space Nontrivial Solution Heisenberg Group Spherical Function Geodesic Ball
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