On the convergence of rational approximations of semigroups on intermediate spaces

Kovács, Mihály

doi:10.1090/S0025-5718-06-01905-3

On the convergence of rational approximations of semigroups on intermediate spaces
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Math. Comp. 76 (2007), 273-286 Request permission

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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