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TitleHarmonic analysis and hypercomplex function theory in co-dimension one
Author(s)Malonek, Helmuth R.
Cação, Isabel
Falcão, M. I.
Tomaz, Graça
KeywordsClifford algebras
Hypercomplex Appell polynomials
Hypercomplex derivative
Hypercomplex differential forms
Issue date2019
JournalSpringer Proceedings in Mathematics and Statistics
Abstract(s)Fundamentals of a function theory in co-dimension one for Clifford algebra valued functions over ℝn+1 are considered. Special attention is given to their origins in analytic properties of holomorphic functions of one and, by some duality reasons, also of several complex variables. Due to algebraic peculiarities caused by non-commutativity of the Clifford product, generalized holomorphic functions are characterized by two different but equivalent properties: on one side by local derivability (existence of a well defined derivative related to co-dimension one) and on the other side by differentiability (existence of a local approximation by linear mappings related to dimension one). As important applications, sequences of harmonic Appell polynomials are considered whose definition and explicit analytic representations rely essentially on both dual approaches.
TypeConference paper
Publisher version
AccessOpen access
Appears in Collections:CMAT - Artigos em atas de conferências e capítulos de livros com arbitragem / Papers in proceedings of conferences and book chapters with peer review

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