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$ L\sp{p}$-estimates for matrix coefficients of irreducible representations of compact groups

Authors: Saverio Giulini and Giancarlo Travaglini
Journal: Proc. Amer. Math. Soc. 80 (1980), 448-450
MSC: Primary 22E45; Secondary 43A75
MathSciNet review: 581002
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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 $ \pi $ of G there exists a matrix coefficient $ {a_\pi }$ of $ \pi $ such that

$\displaystyle {A_p} < {d_\pi }\int_G {\vert{a_\pi }{\vert^p} < {B_p}} $

where $ {d_\pi }$ is the degree of $ \pi $.

As an application we show the nonexistence of infinite local $ {\Lambda _q}$-sets.

References [Enhancements On Off] (What's this?)

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Keywords: Semisimple Lie groups, representations, weights
Article copyright: © Copyright 1980 American Mathematical Society

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