<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

Data publikacji: 10 gru 2014

Zakres stron: 221 - 235

Otrzymano: 01 gru 2013

Przyjęty: 01 sty 2014

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

Słowa kluczowe
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

Data publikacji: 10 gru 2014

Zakres stron: 221 - 235

Otrzymano: 01 gru 2013

Przyjęty: 01 sty 2014

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

Słowa kluczoweCommutative 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.

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