Hadamard product of bases of polynomials in clifford analysis^∗

^∗The final version of this paper was prepared when the author was visiting the Department of Pure Mathematics and Computer Algebra, State University of Gent, Belgium.

Abstract

This paper is concerned with the extension of the notion of Hadamard product of bases of polynomials in one complex variable to the setting of Clifford analysis. It is proposed to study the effect of the algebraic property of a Hadamard product base of special monogenic polynomials on its convergence properties. Unlike the complex case some of these convergence properties may not be interchanged.

Keywords:

• Clifford valued functions
• Polynomial basis
• Hadamard product

AMS Subject Classfications::

• 30G35
• 41A10

^∗The final version of this paper was prepared when the author was visiting the Department of Pure Mathematics and Computer Algebra, State University of Gent, Belgium.

^† [email protected], [email protected]

^∗The final version of this paper was prepared when the author was visiting the Department of Pure Mathematics and Computer Algebra, State University of Gent, Belgium.

^† [email protected], [email protected]

Notes

^∗The final version of this paper was prepared when the author was visiting the Department of Pure Mathematics and Computer Algebra, State University of Gent, Belgium.

^† [email protected], [email protected]