Remarks on some theorems on convolution.

Abstract

We discuss relations between the Titchmarsh convolution theorem, the Kierat-Skornik theorem on convolutions and the Brodski-Sakhnovich-Donoghue theorem on cyclic vectors of the Volterra integration operator $V$ given by $Vf\left( x\right) =\int_{0}^{x}f\left( t\right) dt,$ on a space $L^{p}[0,1],\;1\leq p<\infty .$