The following result is proved. Theorem. Let G be a compact connected semisimple Lie group. For any p > 0 there exist two positive numbers Ap and Bq such that (up to equivalence) for any continuous irreducible unitary representation π of G there exists a matrix coefficient aw of π such that Ap < dw ∫ |a|p > Bp where dw is the degree of π. As an application we show the nonexistence of infinite local ;q-sets
Giulini, S., Travaglini, G. (1980). L^p estimates for matrix coefficients of irreducible representations of compact groups. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 80(3), 448-450 [10.1090/S0002-9939-1980-0581002-9].
L^p estimates for matrix coefficients of irreducible representations of compact groups
TRAVAGLINI, GIANCARLO
1980
Abstract
The following result is proved. Theorem. Let G be a compact connected semisimple Lie group. For any p > 0 there exist two positive numbers Ap and Bq such that (up to equivalence) for any continuous irreducible unitary representation π of G there exists a matrix coefficient aw of π such that Ap < dw ∫ |a|p > Bp where dw is the degree of π. As an application we show the nonexistence of infinite local ;q-sets
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