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 L^p norms of higher rank eigenfunctions and bounds for spherical functions


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We prove almost sharp upper bounds for the L^p norms of eigenfunctions of the full ring of invariant differential operators on a compact locally symmetric space. Our proof combines techniques from semiclassical analysis with harmonic theory on reductive groups, and makes use of new asymptotic bounds for spherical functions that are of independent interest.



Author: Simon Marshall

Source: https://archive.org/



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