Approximative approach to fractional powers of operators. (English) Zbl 1059.47501
Begehr, Heinrich G. W. (ed.) et al., Proceedings of the second ISAAC congress. Vol. 2. Proceedings of the International Society for Analysis, its Applications and Computation Congress, Fukuoka, Japan, August 16–21, 1999. Dordrecht: Kluwer Academic Publishers (ISBN 0-7923-6598-4/hbk). Int. Soc. Anal. Appl. Comput. 8, 1163-1170 (2000).
Summary: A new formula is obtained for fractional powers of operators in a Banach space (which are generators of strongly continuous uniformly bounded semigroups ). This formula is based on the so-called approximative approach and represents the fractional power as a limit of “nice” operators of the form with the elementary function .
|47A60||Functional calculus of operators|
|47A58||Operator approximation theory|
|47D06||One-parameter semigroups and linear evolution equations|
|26A33||Fractional derivatives and integrals (real functions)|