Hermitian Clifford analysis and resolutions

Abstract

SUMMARYIn this paper, we discuss the so-called Witt basis in a Cli ord algebra and we axiomatically deÿne an algebra of abstract Hermitian vector variables similar to the 'radial algebra'. In this setting, we introduce some linear partial di erential operators and we study their resolutions.

Elements of Metrodynamics: the General Setting

“…leaving invariant the spaces We conclude that a truely Sp(n)-invariant biregular system might consist of operators ∂ x , ∂ x| and ∂ y (and/or ∂ y| ) or for example system (19) or (20).…”

“…Another generalization can be achieved by complexifying the vector variables and the Clifford algebra, obtaining the framework of the so-called Hermitian Clifford analysis, see [2,3,16,19]. Let us consider the complex Clifford algebra C m endowed with the Witt basis.…”

Generalized Taylor series in hermitian Clifford analysis

“…We refer to this setting as the Euclidean one, since the fundamental group leaving the Dirac operator ∂ invariant is the special orthogonal group SO(m; R), which is doubly covered by the Spin(m) group of the Clifford algebra R 0,m . In case the dimension m is even, say m = 2n, so-called hermitian Clifford analysis was recently introduced as a refinement of Euclidean Clifford analysis (see the books [44,25] and the series of papers [45,28,5,6,18,29,11]). The considered functions now take values in the complex Clifford algebra C 2n or in complex spinor space S n .…”

On the Structure of Complex Clifford Algebra

“…A systematic development of this function theory, including the invariance properties with respect to the underlying Lie groups and Lie algebras, is still in full progress, see e.g. [10,1,2,7,9,3,4,24,13].…”