On logarithmic residue of monogenic functions in a three-dimensional commutative algebra with one-dimensional radical-Reference-Cited by-同舟云学术

On logarithmic residue of monogenic functions in a three-dimensional commutative algebra with one-dimensional radical

Published:2017-12-20 Issue:3 Volume:25 Page:167-182
ISSN:1844-0835
Container-title:Analele Universitatii "Ovidius" Constanta - Seria Matematica
language:en
Short-container-title:

Author:

Pukhtaievych Roman¹,Plaksa Sergiy²

Affiliation:

1. Department of Mathematics "Tullio Levi-Civita", University of Padova, 63, Via Trieste, Padova , Italy

2. Department of complex analysis and potential theory, Institute of Mathematics of the National Academy of Sciences of Ukraine, 3, Tereshchenkivska st., Kiev , Ukraine

Abstract

Abstract We consider monogenic functions taking values in a three-dimensional commutative algebra A2 over the field of complex numbers with one- dimensional radical. We calculate the logarithmic residues of monogenic functions acting from a three-dimensional real subspace of A2 into A2. It is shown that the logarithmic residue depends not only on zeros and singular points of a function but also on points at which the function takes values in ideals of A2, and, in general case, is a hypercomplex number.

Publisher

Walter de Gruyter GmbH

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