Displaying similar documents to “Canonical bases for 𝔰𝔩 ( 2 , ℂ ) -modules of spherical monogenics in dimension 3”

Fischer decompositions in Euclidean and Hermitean Clifford analysis

Freddy Brackx, Hennie de Schepper, Vladimír Souček (2010)

Archivum Mathematicum

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Euclidean Clifford analysis is a higher dimensional function theory studying so–called monogenic functions, i.e. null solutions of the rotation invariant, vector valued, first order Dirac operator ∂ ̲ . In the more recent branch Hermitean Clifford analysis, this rotational invariance has been broken by introducing a complex structure J on Euclidean space and a corresponding second Dirac operator ∂ ̲ J , leading to the system of equations ∂ ̲ f = 0 = ∂ ̲ J f expressing so-called Hermitean monogenicity. The invariance...

The Real Vector Spaces of Finite Sequences are Finite Dimensional

Yatsuka Nakamura, Artur Korniłowicz, Nagato Oya, Yasunari Shidama (2009)

Formalized Mathematics

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In this paper we show the finite dimensionality of real linear spaces with their carriers equal Rn. We also give the standard basis of such spaces. For the set Rn we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal n.MML identifier: EUCLID 7, version: 7.11.01 4.117.1046