Basic sets of pofynomials in clifford analysis
Mahmoud Abul-Ez, Denis Constales · Complex Variables Theory and Application An International Journal · 1990
This paper is concerned with the extension of the theory of basic sets of polynomials in one complex variable, as introduced by J. M. Whittaker and B. Cannon, to the setting of Clifford analysis. This is the natural generalization of complex analysis to Euclidean space of dimension larger than two, where the regular functions have values in a Clifford algebra and are null-solutions of a linear differential operator which linearizes the laplacian. An important subclass of the Clifford regular functions are considered, for which a Cannon theorem on the effectiveness in closed balis is proved This result is consequently refined in terms of the order and type of entire functions in this subclass.