The Fischer Decomposition for the H-action and Its Applications
Roman Lavicka
TL;DR
This paper explores the Fischer decomposition related to the H-action of the Pin group on Clifford algebra valued polynomials, applying it to decompose special monogenic polynomials into two-sided monogenic components.
Contribution
It introduces new decompositions of monogenic and inframonogenic polynomials using the Fischer decomposition for the H-action, expanding understanding of polynomial structures in Clifford analysis.
Findings
Decomposition of special monogenic polynomials into two-sided monogenic parts
Application of Fischer decomposition to inframonogenic polynomials
Enhanced understanding of polynomial structures in Clifford analysis
Abstract
Recently the Fischer decomposition for the H-action of the Pin group on Clifford algebra valued polynomials has been obtained. We apply this tool to get various decompositions of special monogenic and inframonogenic polynomials in terms of two sided monogenic ones.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic and Geometric Analysis · Algebraic structures and combinatorial models