Suppose G is a n-dimensional compact connected semisimple Lie group and DR is the spherical Dirichlet kernel on G. We prove the existence of a positive constant K such that ∥DR∥1 ≥ KR (n - 1) 2 This complements the known result ∥DR∥1 ≤ HR (n - 1) 2. We also prove that for a polyhedral Dirichlet kernel DN the above inequalities hold with Np in place of R (n - 1) 2 (p is the number of positive roots of G). © 1986.
Giulini, S., Travaglini, G. (1986). Sharp estimates for Lebesgue constants on compact Lie groups. JOURNAL OF FUNCTIONAL ANALYSIS, 68(1), 106-116 [10.1016/0022-1236(86)90059-5].
Sharp estimates for Lebesgue constants on compact Lie groups
TRAVAGLINI, GIANCARLO
1986
Abstract
Suppose G is a n-dimensional compact connected semisimple Lie group and DR is the spherical Dirichlet kernel on G. We prove the existence of a positive constant K such that ∥DR∥1 ≥ KR (n - 1) 2 This complements the known result ∥DR∥1 ≤ HR (n - 1) 2. We also prove that for a polyhedral Dirichlet kernel DN the above inequalities hold with Np in place of R (n - 1) 2 (p is the number of positive roots of G). © 1986.
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