Abstract: | We find expressions and estimates for integer powers of the differentiation operator in noncommuting directions for analytic functions of sectorial operators on a complex Banach space. We study the exponential of such a differentiation operator and give an application to the theory of perturbations of evolution equations.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 70–74. |