The following result is proved. THEOREM. Let G be a compact connected semisimple Lie group. For any p > 0 there exist two positive numbers A_p and B_p such that (up to equivalence) for any continuous irreducible unitary representation π of G there exists a matrix coefficient a_π of π such that A_p < d_π ∫|a_π|^p < B_p where d_π is the degree of π. As an application we show the nonexistence of infinite local Λ_q-sets.

Lp-estimates for matrix coefficients of irreducible representations of compact Lie groups

GIULINI, SAVERIO;
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 A_p and B_p such that (up to equivalence) for any continuous irreducible unitary representation π of G there exists a matrix coefficient a_π of π such that A_p < d_π ∫|a_π|^p < B_p where d_π is the degree of π. As an application we show the nonexistence of infinite local Λ_q-sets.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11567/390741
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