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Hermite functions on compact Lie groups. I. (English) Zbl 0836.43016
The formula for Hermite polynomials on R d is well known as well as the existence of a linear isometry of S ¯ onto L 2 (R d ,p 1 ); S=S(C d ) denotes the vector space of symmetric tensors over C d , 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.

MSC:
43A77Analysis on general compact groups
33C45Orthogonal polynomials and functions of hypergeometric type
22E30Analysis on real and complex Lie groups