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

S. A. Plaksa; R. P. Pukhtaievych

doi:10.2478/auom-2014-0018

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

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

Volume 22 (2014): Issue 1 (March 2014)

By: S. A. Plaksa and R. P. Pukhtaievych

Open Access

|Dec 2014

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.

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Articles in this issue

DOI: https://doi.org/10.2478/auom-2014-0018 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784

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Language: English

Page range: 221 - 235

Submitted on: Dec 1, 2013

Accepted on: Jan 1, 2014

Published on: Dec 10, 2014

Published by: Ovidius University of Constanta

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Commutative Banach algebra,

monogenic function,

Laplace equation,

Cauchy integral theorem,

Cauchy integral formula,

Morera theorem

Related subjects:

Mathematics,

General mathematics

© 2014 S. A. Plaksa, R. P. Pukhtaievych, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 22 (2014): Issue 1 (March 2014)