Algebraic Methods in Partial Differential Operators

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Abstract

In this paper we build a class of partial differential operators L having the following property : if u is a meromorphic function in \mathbb{C}^n and Lu is a rational function \frac{A}{q}, with q homogenous, then u is also a rational function.

Keywords:

Chow's lemma;regular partial differential operators;meromrphic functions;homogeneous polynomials;Euler's differential operator
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Algebraic Methods in Partial Differential Operators. (2005). Journal of Partial Differential Equations, 18(2), 114-120. https://www.global-sci.com/index.php/jpde/article/view/4037