FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 4, PAGES 1177-1186

On the class of semigroups of linear bounded operators

Y. T. Silchenko

Abstract

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The semigroup of linear bounded operators admitting a singularity not connected with a singularity of the derivative of the semigroup is considered, where the generator of the semigroup may have non-dense domain. Fractional powers of the generator are studied and the theorem of Cauchy problem solvability for the differential equation with an operator coefficient is given.

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Last modified: April 17, 2002