Abstract
Suppose G is a n -dimensional compact connected semisimple Lie group and D R is the spherical Dirichlet kernel on G . We prove the existence of a positive constant K such that ∥D R ∥ 1 ⩾ KR (n − 1) 2 This complements the known result ∥D R ∥ 1 ⩽ HR (n − 1) 2 . We also prove that for a polyhedral Dirichlet kernel D N the above inequalities hold with N p in place of R (n − 1) 2 ( p is the number of positive roots of G ).
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