A NOTE ON THE EXPLICIT ANALYTIC SOLUTION TO A NONAUTONOMOUS ABSTRACT EVOLUTION EQUATION

We consider a nonautonomous abstract evolution equation on Banach space. If the evolutionary operator and the evolutionary kernel are real analytic at the initial time there is an explicit formula for the coefficients of the operator in terms of the coefficients of the kernel. In this note we show that the converse is also true by finding an explicit formula for the coefficients of the kernel in terms of the coefficients of the operator.