Abstract
Let G be a non-compact group, K the compact subgroup fixed by a Cartan involution and assume G / K is an exceptional, symmetric space, one of Cartan type E, F or G. We find the minimal integer, L(G), such that any convolution product of L(G) continuous, K-bi-invariant measures on G is absolutely continuous with respect to Haar measure. Further, any product of L(G) double cosets has non-empty interior. The number L(G) is either 2 or 3, depending on the Cartan type, and in most cases is strictly less than the rank of G.
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Communicated by K. Gröchenig.
This research is supported in part by NSERC 45597.
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Hare, K.E., He, J. The absolute continuity of convolution products of orbital measures in exceptional symmetric spaces. Monatsh Math 182, 619–635 (2017). https://doi.org/10.1007/s00605-016-0999-5
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DOI: https://doi.org/10.1007/s00605-016-0999-5