Factoring an entire function into two `almost equal' functions (Q1360837)

The article is concerned with factoring an entire function on the complex plane into the product of two entire functions with almost the same growth at infinity. The main result establishes such a factorization under rather general but bulky conditions. It is concretized in the case when the zeros of the function in question lie in some horizontal strip. As an application, a smooth compactly-supported function on the real axis, having the Fourier-Laplace transform with zeros in a horizontal strip, is proved to be representable as the convolution of two other smooth compactly-supported functions. This gives a partial answer to Ehrenpreis's factorization problem in the algebra of smooth compactly-supported functions of one variable.