HERMITE FUNCTION EXPANSIONS VERSUS HERMITE POLYNOMIAL EXPANSIONS

I. ABU-FALAHAH; J. L. TORREA

doi:10.1017/S0017089506003004

Abstract

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We consider expansions with respect to the multi-dimensional Hermite functions and to the multi-dimensional Hermite polynomials. They are respectively eigenfunctions of the Harmonic oscillator $\cal{L}= -\Delta +|x|^2$ and of the Ornstein-Uhlenbeck operator ${\bf L} = -\Delta +2x \cdot \nabla.$ The corresponding heat semigroups and Riesz transforms are considered and results on both aspects (polynomials and functions) are obtained.

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HERMITE FUNCTION EXPANSIONS VERSUS HERMITE POLYNOMIAL EXPANSIONS

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

HERMITE FUNCTION EXPANSIONS VERSUS HERMITE POLYNOMIAL EXPANSIONS

Abstract

Keywords

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