eprintid: 13298
rev_number: 13
eprint_status: archive
userid: 3588
dir: disk0/00/01/32/98
datestamp: 2014-10-23 09:32:16
lastmod: 2023-02-16 10:51:58
status_changed: 2014-10-23 09:32:16
type: article
metadata_visibility: show
title: Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras
language: english
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.
creators_name: Pogorui, A. A.
creators_name: Rodríguez-Dagnіno, Ramón М.
creators_name: Shapіro, Мichael
ispublished: pub
subjects: QA77
divisions: sch_man
full_text_status: public
date: 2013
publication: Math. Meth. Appl. Sci.
publisher: John Wiley & Sons
refereed: TRUE
citation:   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..       
document_url: http://eprints.zu.edu.ua/13298/1/2013-mma.Solution_PDE.pdf