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On the convergence of rational approximations of semigroups on intermediate spaces

Author: Mihály Kovács
Journal: Math. Comp. 76 (2007), 273-286
MSC (2000): Primary 65J10; Secondary 65M12, 46N40, 46B70
Published electronically: October 4, 2006
MathSciNet review: 2261021
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Abstract: We generalize a result by Brenner and Thomée on the rate of convergence of rational approximation schemes for semigroups. Using abstract interpolation techniques we obtain convergence on a continuum of intermediate spaces between the Banach space $ X$ and the domain of a certain power of the generator of the semigroup. The sharpness of the results is also discussed.

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Additional Information

Mihály Kovács
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803 and Department of Analysis, Mathematics Institute, University of Miskolc, Miskolc-Egyetemváros, Hungary, H-3515
Address at time of publication: Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin, New Zealand

Keywords: Rational approximation of semigroups, intermediate spaces, Favard spaces, Hille-Phillips functional calculus, time-discretization
Received by editor(s): September 7, 2005
Published electronically: October 4, 2006
Article copyright: © Copyright 2006 American Mathematical Society