<abstract xmlns="http://www.w3.org/1999/xhtml"> 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. </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.

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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We consider monogenic functions taking values in a three-dimensional commutative algebra A2 over the field of complex numbers with one- dimensional radical. We...

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

Published Online: Mar 31, 2018

Page range: 167 - 182

Received: Dec 20, 2016

Accepted: Feb 20, 2017

DOI: https://doi.org/10.1515/auom-2017-0043

Keywords
Commutative Banach algebra, monogenic function, logarithmic residue

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Mar 31, 2018

Page range: 167 - 182

Received: Dec 20, 2016

Accepted: Feb 20, 2017

DOI: https://doi.org/10.1515/auom-2017-0043

KeywordsCommutative Banach algebra, monogenic function, logarithmic residue

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
Commutative Banach algebra, monogenic function, logarithmic residue