Hermitean Téodorescu transform decomposition of continuous matrix functions on fractal hypersurfaces.

Abreu-Blaya, Ricardo; Bory-Reyes, Juan; Brackx, Fred; De Schepper, Hennie

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Hermitean Cauchy integral decomposition of continuous functions on hypersurfaces.

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Extension theorem for complex Clifford algebras-valued functions on fractal domains.

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A generalization of the Schwarzian via Clifford numbers.

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Generalized Moisil-Théodoresco systems and Cauchy integral decompositions.

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Clifford algebra with Reduce

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Szegő projections for Hardy spaces of monogenic functions and applications.

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Morera type problems in Clifford analysis.

Emilio Marmolejo Olea (2001)

Revista Matemática Iberoamericana

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The Pompeiu and the Morera problems have been studied in many contexts and generality. For example in different spaces, with different groups, locally, without an invariant measure, etc. The variations obtained exhibit the fascination of these problems. In this paper we present a new aspect: we study the case in which the functions have values over a Clifford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations....

Clifford-Hermite-monogenic operators

Freddy Brackx, Nele de Schepper, Frank Sommen (2006)

Czechoslovak Mathematical Journal

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In this paper we consider operators acting on a subspace $ℳ$ of the space $L_{2} (ℝ^{m}; ℂ_{m})$ of square integrable functions and, in particular, Clifford differential operators with polynomial coefficients. The subspace $ℳ$ is defined as the orthogonal sum of spaces $ℳ_{s, k}$ of specific Clifford basis functions of $L_{2} (ℝ^{m}; ℂ_{m})$ . Every Clifford endomorphism of $ℳ$ can be decomposed into the so-called Clifford-Hermite-monogenic operators. These Clifford-Hermite-monogenic operators are characterized in terms of commutation relations...