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Title: Harmonic Analysis and hypercomplex function theory in co-dimension one
Author: Malonek, Helmuth R.
Cação, Isabel
Falcão, M. Irene
Tomaz, Graça
Keywords: Clifford algebras
Hypercomplex differential forms
Hypercomplex derivative
Hypercomplex Appell polynomials
Issue Date: 29-Aug-2019
Publisher: Springer Nature Switzerland AG 2019
Abstract: Fundamentals of a function theory in co-dimension one for Clifford algebra valued functions over R^(n+1) are considered. Special attention is given to theirorigins 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 arecharacterized 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 theother 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.
Peer review: yes
DOI: 10.1007/978-3-030-26748-3_7
ISBN: 978-3-030-26747-6
Appears in Collections:CIDMA - Capítulo de livro
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