Coherent states and uncertainty relations

TL;DR

This paper discusses the estimation of $L^p$-norms of matrix coefficients in square integrable representations, proposing a conjecture and providing a proof for integer $p$ values using Burbea's result.

Contribution

It introduces a conjecture on $L^p$-norms of matrix coefficients and proves it for integer $p$ using existing mathematical results.

Findings

Conjecture on $L^p$-norms of matrix coefficients.

Proof of the conjecture for integer $p$ values.

Application of Burbea's result to representation theory.

Abstract

A sharp estimation of the $L^p$-norms of some matrix coefficients of the square integrable representations is conjectured. The conjecture can be proved for integer values of $p$ using a result of J. Burbea.