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Zbl 0836.43016
Hijab, Omar
Hermite functions on compact Lie groups. I.
(English)
[J] J. Funct. Anal. 125, No.2, 480-492 (1994). ISSN 0022-1236

The formula for Hermite polynomials on $R^d$ is well known as well as the existence of a linear isometry of $\overline {S}$ onto $L^2(R^d, p_1)$; $S = S(C^d)$ denotes the vector space of symmetric tensors over $C^d$, $\overline{S}$ is the completion of $S$ in a precise inner product, and $p_1(x)$ is the standard Gaussian on $R^d$. By L. Gross the above problem was extended to the case where $R^d$ is replaced by a compact Lie group $G$. The author exhibits explicitly, in a new and more convenient manner, the isometry proved by L. Gross. -- Mention must be made of the remarks 2.7, 3.2 and 3.4.
[O.Costinescu (Iaşi)]
MSC 2000:
*43A77 Analysis on general compact groups
33C45 Orthogonal polynomials and functions of hypergeometric type
22E30 Analysis on real and complex Lie groups

Keywords: Hermite polynomials; linear isometry; symmetric tensors; compact Lie group

Cited in: Zbl 0971.22008 Zbl 0843.43010

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