The principal result of this paper is a proof of the Convolution Theorem based on the definition of a convolution operator as presented by E. M. Stein and R. O'Neil. Closely related are earlier ...

A nonlinear version of Ovcyannikov's theorem is proved. If $F(u, t)$ is an analytic function of $t$ real or complex and of $u$ varying in a scale of Banach spaces ...