Geodesic
HERMITE FUNCTION EXPANSIONS VERSUS HERMITE POLYNOMIAL EXPANSIONS
Glasgow mathematical journal, Tome 48 (2006) no. 2, pp. 203-215

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DOI

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.
DOI : 10.1017/S0017089506003004
Mots-clés : 42C10, 42B20, 42B25 
ABU-FALAHAH, I.; TORREA, J. L. HERMITE FUNCTION EXPANSIONS VERSUS HERMITE POLYNOMIAL EXPANSIONS. Glasgow mathematical journal, Tome 48 (2006) no. 2, pp. 203-215. doi: 10.1017/S0017089506003004
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     title = {HERMITE {FUNCTION} {EXPANSIONS} {VERSUS} {HERMITE} {POLYNOMIAL} {EXPANSIONS}},
     journal = {Glasgow mathematical journal},
     pages = {203--215},
     year = {2006},
     volume = {48},
     number = {2},
     doi = {10.1017/S0017089506003004},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089506003004/}
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