%A A. A. Pogorui
%A Ram?n ?. Rodr?guez-Dagn?no
%A ?ichael Shap?ro
%J Math. Meth. Appl. Sci.
%T Solutions for PDEs with constant coefficients and derivability of functions ranged in commutative algebras
%X 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.
%D 2013
%I John Wiley & Sons
%L zu213298