Hermitean Clifford-Hermite polynomials. (English) Zbl 1134.30039

As part of a program to develop the Hermitean setting of Clifford analysis the authors introduce Hermitean Clifford-Hermite polynomials. They start with a report on the (usual) radial Clifford-Hermite polynomials and they then give the necessary background of the Hermitean setting of Clifford analysis. The definition of the Hermitean Clifford-Hermite polynomials leads to four different types of these polynomials, two of even degree und two of odd degree. The recurrence relations, explicit forms, and orthogonality relations are given, clearly this is rich on formulas. An outlook points to Hermitean Clifford-Hermite functions and to applications to wavelet kernels.


30G35 Functions of hypercomplex variables and generalized variables
33E30 Other functions coming from differential, difference and integral equations
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