Chain-finite operators and locally chain-finite operators.
The problem we are concerned with in this research announcement is the algebraic characterization of chain-finite operators (global case) and of locally chain-finite operators (local case).
The problem we are concerned with in this research announcement is the algebraic characterization of chain-finite operators (global case) and of locally chain-finite operators (local case).
In this paper we consider operators acting on a subspace of the space of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace is defined as the orthogonal sum of spaces of specific Clifford basis functions of . Every Clifford endomorphism of 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...