Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras

Pogoruі, А. А. and Rodríguez-Dagnіno, Ramón М. and Shapіro, Мichael (2013) Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras. Math. Meth. Appl. Sci..

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Abstract

It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper, we extend this idea to finite-dimensional commutative algebras; that is, we prove that if some basis of a subspace of a commutative algebra satisfies a polynomial equation, then the components of a monogenic function on the subspace are solutions of the respective partial differential equation (PDE). We illustrate these concepts with a few examples.

Item Type: Article
Subjects: Q Science > QA Mathematics > Mathematical Analysis
Divisions: Faculty of Physics and Mathematics > Department of Mathematical Analysis
Depositing User: Ірина Ігорівна Таргонська
Date Deposited: 23 Oct 2014 09:32
Last Modified: 15 Aug 2015 09:15
URI: http://eprints.zu.edu.ua/id/eprint/13298

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