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arXiv · 0811.2555

Solution of Partial Differential Equations by Method of Hyperholomorphic functions

Anatoliy A. Pogorui
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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 generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a subspace of a commutative algebra satisfies a polynomial equation then components of a hyperholomorphic function on the subspace are solutions of the respective partial differential equation.

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Anatoliy A. Pogorui. 2008-11-16. Solution of Partial Differential Equations by Method of Hyperholomorphic functions. https://arxiv.org/abs/0811.2555

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