Mathematics of Computation

On the convergence of rational approximations of semigroups on intermediate spaces

Author(s): Mihály Kovács.
Journal: Math. Comp. 76 (2007), 273-286.
MSC (2000): Primary 65J10; Secondary 65M12, 46N40, 46B70
Posted: October 4, 2006
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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

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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Retrieve articles in Mathematics of Computation with MSC (2000): 65J10, 65M12, 46N40, 46B70

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
Email: kmisi@math.lsu.edu

DOI: 10.1090/S0025-5718-06-01905-3
PII: S 0025-5718(06)01905-3
Keywords: Rational approximation of semigroups, intermediate spaces, Favard spaces, Hille-Phillips functional calculus, time-discretization
Received by editor(s): September 7, 2005
Posted: October 4, 2006
Copyright of article: Copyright 2006, American Mathematical Society

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