Factorization of Solutions of Convolution Equations II

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Let C=(Rn), be the vector space of complex valued C functions on Rn. It is well known (from the fundamental Principle of Ehrenpreis for the case n > 1 and more easily, from the classical Euler exponential polynomial representation of solutions of ordinary differential equations, for the case n 1) that if the partial differential equation (0.1) Q(D)f =O is such that Q C[Zl,..., Zn] can be factored as Q Q1 Q2, with Q1 and Q2 relatively prime, then every C solution of (0.1) can be written as f fl / rE, with Qi(D)fi 0, i= 1,2. The natural extension of the previous


This article was originally published in Illinois Journal of Mathematics , volume 35, in 1991.

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