Abstract
Let be a Banach space and a non-increasing function such that as and is a Lipschitz function on . A linear operator is said to be -sectorial if there exist constants and such that the spectrum of lies in the set and there exists such that for where is the resolvent of the operator . The properties of the operator exponential and fractional powers of a -sectorial operator are analysed alongside the question of the unique solubility of the Cauchy problem for the linear differential operator with -sectorial operator-valued coefficient.
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