Titlebook: Hypercomplex Analysis: New Perspectives and Applications; Swanhild Bernstein,Uwe K?hler,Frank Sommen Conference proceedings 2014 Springer

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Fractional Clifford Analysis,In this paper we present the basic tools of a fractional function theory in higher dimensions by means of a fractional correspondence to the Weyl relations. A Fischer decomposition, Almansi decomposition, fractional Euler and Gamma operators, monogenic projection, and basic fractional homogeneous powers will be constructed.

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Spectral Properties of Differential Equations in Clifford Algebras,The aim of this work is to establish a number of elementary properties about the topology and algebra of real quadratic homogeneous mappings and Riccati type ODEs occurring in Clifford Algebras. We construct an example of the quadratic vector field to show the impact of the spectral properties on qualitative theory.

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Differential Equations in Multicomplex Spaces,We use Ehrenpreis’ Fundamental Principle to give different representations of holomorphic functions in multicomplex spaces, and we give the first elements of a theory of constant coefficients differential equations, of finite and infinite order, in the multicomplex setting.

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