<abstract xmlns="http://www.w3.org/1999/xhtml"><p>We obtain a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of holomorphic functions of the complex variable. We prove that the mentioned monogenic functions have the Gateaux derivatives of all orders. For monogenic functions we prove also analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, the Morera theorem and the Cauchy integral formula.</p></abstract>

We obtain a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of holomorphic functions of the complex variable. We prove that the mentioned monogenic functions have the Gateaux derivatives of all orders. For monogenic functions we prove also analogues of classical integral theorems of the holomorphic function theory: the Cauchy integral theorems for surface and curvilinear integrals, the Morera theorem and the Cauchy integral formula.

Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra"}

We obtain a constructive description of monogenic functions taking values in a finite-dimensional semi-simple commutative algebra by means of holomorphic...

Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra

Published Online: Dec 10, 2014

Page range: 221 - 235

Received: Dec 01, 2013

Accepted: Jan 01, 2014

DOI: https://doi.org/10.2478/auom-2014-0018

Keywords
Commutative Banach algebra, monogenic function, Laplace equation, Cauchy integral theorem, Cauchy integral formula, Morera theorem

© 2014 S. A. Plaksa and R. P. Pukhtaievych

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Monogenic Functions in a Finite-Dimensional Semi-Simple Commutative Algebra

Published Online: Dec 10, 2014

Page range: 221 - 235

Received: Dec 01, 2013

Accepted: Jan 01, 2014

DOI: https://doi.org/10.2478/auom-2014-0018

KeywordsCommutative Banach algebra, monogenic function, Laplace equation, Cauchy integral theorem, Cauchy integral formula, Morera theorem

© 2014 S. A. Plaksa and R. P. Pukhtaievych

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Commutative Banach algebra, monogenic function, Laplace equation, Cauchy integral theorem, Cauchy integral formula, Morera theorem