relation: http://eprints.zu.edu.ua/13298/
title: Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras
creator: Pogorui, A. A.
creator: Rodríguez-Dagnіno, Ramón М.
creator: Shapіro, Мichael
subject: Математичний аналіз
description: 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.
publisher: John Wiley & Sons
date: 2013
type: Стаття
type: PeerReviewed
format: text
language: uk
identifier: http://eprints.zu.edu.ua/13298/1/2013-mma.Solution_PDE.pdf
identifier:   Pogorui, A. A., Rodríguez-Dagnіno, Ramón М., Shapіro, Мichael  (2013) Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras.  Math. Meth. Appl. Sci..       
language: english