NECESSARY AND SUFFICIENT CONDITIONS FOR HYPOELLIPTICITY FOR A CLASS OF CONVOLUTION-OPERATORS

In this paper the Corwin's conjecture is proved, which says that if d is a function analytic near infinity, then the hypoellipticity of the convolution operator A(d), defined by A(d)u = du for every u is-an-ele ment-of S'(R(n)), implies that P(x)/log x --> infinity as x --> infini ty, where P(x) is the distance from x is-an-element-of R(n) to the set of complex zeros of d.