HARDY'S INEQUALITIES FOR HERMITE AND LAGUERRE EXPANSIONS

YUICHI KANJIN

doi:10.1112/S0024609396002627

Abstract

The well-known inequality of Hardy for Fourier coefficients of functions f(t)∼[sum ]∞n=−∞bneint in the real Hardy space is [sum ]∞n= −∞[mid ]bn[mid ]/([mid ]n[mid ]+1)<∞. We shall establish analogues of this inequality for the Hermite function expansions and also for the Laguerre function expansions.

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HARDY'S INEQUALITIES FOR HERMITE AND LAGUERRE EXPANSIONS

Abstract

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HARDY'S INEQUALITIES FOR HERMITE AND LAGUERRE EXPANSIONS

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