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In this paper, we study the Bargmann–Radon transform and a class of monogenic functions called axially monogenic functions. First, we compute the explicit formula of the Bargmann–Radon transform for axially monogenic functions, by making use of the Funk–Hecke theorem. Then we present the explicit form of the general Cauchy–Kowalewski extension for radial function. Finally, by making use of the results we obtained, we give an application of the Bargmann–Radon transform for Cauchy–Kowalewski extension. [ABSTRACT FROM AUTHOR]

In this article, we solve the Dirichlet boundary value problemwhereis a cylindrical domain,Dis the Cauchy-Riemann operator,is a Clifford algebra-valued function,,,is ak-dimensional submanifold of the boundary,,is a fixed point inside the domain. If the boundary data are Hölder continuously differentiable functions, then the unique solution is Hölder continuous. We shall prove an estimate of the solution by its boundary data. [ABSTRACT FROM AUTHOR]

In this article, we obtain an explicit expression of the difference and sum of the unit base in the Clifford analysis case by using the analogy with the complex one. These formulae then lead to the introduction of a class of Bernoulli polynomials in the Clifford analysis setting which are linked to the sum base. The newly introduced Bernoulli polynomials have properties which are very similar to those of the classical ones. Then we prove that each of the sum and difference of the unit base is of order 1. Finally, certain convergence properties of the difference and sum of simple monic bases of special monogenic polynomials are investigated. The obtained results generalize the complex case proved by Mikhail and Nassif to the Clifford setting. [ABSTRACT FROM PUBLISHER]

The main goal of this article is to study special polynomial power series expansions for entire axially monogenic functions. In relation to the difference and sum bases of monogenic polynomials, which have link with Bernoulli polynomials, the best possible bounds for the orders of such bases are determined. Moreover the Tρ-property of such differenced base and the sum base is discussed. The results obtained contain previous ones of complex setting as special cases. [ABSTRACT FROM AUTHOR]

In this article we present a closed formula for the CK-extension of the Gaussian distribution in m, and the monogenic version of the holomorphic function [image omitted] which is a fundamental solution of the generalized Cauchy-Riemann operator. [ABSTRACT FROM AUTHOR]

In this article, half Robin problems for powers of Dirac operator in the unit ball B of Rm (m x≥ 3) are investigated. By using a certain kind of decomposition of k-monogenic functions an explicit formula for the solution and the necessary and sufficient conditions for the solvability of the problems are obtained. [ABSTRACT FROM AUTHOR]