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.
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Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 70–74.
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Lopushans'kii, A.O. Differentiation of analytic functions of sectorial operators in noncommuting directions. J Math Sci 96, 2999–3002 (1999). https://doi.org/10.1007/BF02169695
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DOI: https://doi.org/10.1007/BF02169695