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Clifford-Hermite-monogenic operators

Freddy Brackx; Nele de Schepper; Frank Sommen — 2006

Czechoslovak Mathematical Journal

In this paper we consider operators acting on a subspace $ℳ$ of the space $L_{2} (ℝ^{m}; ℂ_{m})$ of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace $ℳ$ is defined as the orthogonal sum of spaces $ℳ_{s, k}$ of specific Clifford basis functions of $L_{2} (ℝ^{m}; ℂ_{m})$ . Every Clifford endomorphism of $ℳ$ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic operators are characterized in terms of commutation relations and they...

Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space.

Brackx, Fred; De Schepper, Nele; Sommen, Frank — 2004

International Journal of Mathematics and Mathematical Sciences

Page 1

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