Matrix representations of a special polynomial sequence in arbitrary dimension

This paper provides an insight into different structures of a special polynomial sequence of binomial type in higher dimensions with values in a Clifford algebra. The elements of the special polynomial sequence are homogeneous hypercomplex differentiable (monogenic) functions of different degrees and their matrix representation allows to prove their recursive construction in analogy to the complex power functions. This property can somehow be considered as a compensation for the loss of multiplicativity caused by the non-commutativity of the underlying algebra.Fundação para a Ciência e a Tecnologia (FCT

On the convergence properties of basic series representing Clifford valued functions

It is shown that certain classes of special monogenic functions cannot be represented by the basic series in the whole space. New definitions for the order of basis of special monogenic polynomials are given, together with theorems on the representation of classes of special monogenic functions in certain balls and at a point

The µ-th root base of non-algebraic simple base of polynomials in Clifford setting

The present paper is a continuation of our paper [4]. The problem to be studied is the non-impact of algebraic property on the convergence properties of the mu-th root base of special monogenic polynomials. These convergence properties are the investigation of the relation between the effectiveness in closed balls of a given base and that of its mu-th root base, and also the relation between their rate of increase. Our result which is concerned with effectiveness in closed balls is quite different from its corresponding one for the square root case in complex settings

© Hindawi Publishing Corp. ON THE CONVERGENCE PROPERTIES OF BASIC SERIES REPRESENTING CLIFFORD VALUED FUNCTIONS

It is shown that certain classes of special monogenic functions cannot be represented by the basic series in the whole space. New definitions for the order of basis of special monogenic polynomials are given, together with theorems on the representation of classes of special monogenic functions in certain balls and at a point. 2000 Mathematics Subject Classification: 30G35, 41A10. 1. Introduction. Th