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
DOI:
https://doi.org/10.1090/S0025-5718-06-01905-3
Published electronically:
October 4, 2006
MathSciNet review:
2261021
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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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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
Email:
kmisi@math.lsu.edu
DOI:
https://doi.org/10.1090/S0025-5718-06-01905-3
Keywords:
Rational approximation of semigroups,
intermediate spaces,
Favard spaces,
Hille-Phillips functional calculus,
time-discretization
Received by editor(s):
September 7, 2005
Published electronically:
October 4, 2006
Article copyright:
© Copyright 2006
American Mathematical Society