Extension Theorem for Complex Clifford Algebras-Valued Functions on Fractal Domains

Abstract

Monogenic extension theorem of complex Clifford algebras-valued functions over a bounded domain with fractal boundary is obtained. The paper is dealing with the class of Hölder continuous functions. Applications to holomorphic functions theory of several complex variables as well as to that of the so-called biregular functions will be deduced directly from the isotonic approach.

Some Generalized Clifford-Jacobi Polynomials and Associated Spheroidal Wavelets

“…This section is devoted to a brief review on basic concepts on Clifford analysis and fractional calculus as well as the extension of fractional Fourier transforms for the Clifford case. The readers may refer to [1], [2], [8], [9], [10], [12], [15], [16], [19], [33].…”

“…In other words, Clifford algebra generalizes to higher dimensions by the same exact principles applied at lower dimensions, by providing an algebraic entity for scalars, vectors, bivectors, trivectors, and there is no limit to the number of dimensions it can be extended to. More details on Clifford analysis, clifford calculus, origins, history, developments may be found in [1], [12], [14], [28], [25], .…”

New Type of Gegenbauer–Hermite Monogenic Polynomials and Associated Clifford Wavelets

“…In other words, Clifford algebra generalizes to higher dimensions by the same exact principles applied at lower dimensions, by providing an algebraic entity for scalars, vectors, bivectors, trivectors, and there is no limit to the number of dimensions it can be extended to. More details on Clifford algebra, origins, history, developments may be found in [2], [15], [16], [18], [24], [33].…”