Geodesic
$L^p$ norms of higher rank eigenfunctions and bounds for spherical functions
Journal of the European Mathematical Society, Tome 18 (2016) no. 7, pp. 1437-1493.

Voir la notice de l'article provenant de la source EMS Press

We prove almost sharp upper bounds for the Lp norms of eigenfunctions of the full ring of invariant differential operators on a compact locally symmetric space, as well as their restrictions to maximal flat subspaces. 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.
DOI : 10.4171/jems/619
Classification : 22-XX, 35-XX
Keywords: Lp norms, symmetric spaces, spherical functions 
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     author = {Simon Marshall},
     title = {$L^p$ norms of higher rank eigenfunctions and bounds for spherical functions},
     journal = {Journal of the European Mathematical Society},
     pages = {1437--1493},
     publisher = {mathdoc},
     volume = {18},
     number = {7},
     year = {2016},
     doi = {10.4171/jems/619},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/619/}
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Simon Marshall. $L^p$ norms of higher rank eigenfunctions and bounds for spherical functions. Journal of the European Mathematical Society, Tome 18 (2016) no. 7, pp. 1437-1493. doi : 10.4171/jems/619. http://geodesic.mathdoc.fr/articles/10.4171/jems/619/

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