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Journal of Evolution Equations

, Volume 13, Issue 4, pp 875–895 | Cite as

Convergence of subdiagonal Padé approximations of C 0-semigroups

  • Moritz EgertEmail author
  • Jan Rozendaal
Article

Abstract

Let \({(r_{n})_{n \in \mathbb{N}}}\) be the sequence of subdiagonal Padé approximations of the exponential function. We prove that for −A the generator of a uniformly bounded C 0-semigroup T on a Banach space X, the sequence \({(r_{n}(-t A))_{n \in \mathbb{N}}}\) converges strongly to T(t) on D(A α ) for \({\alpha>\frac{1}{2}}\) . Local uniform convergence in t and explicit convergence rates in n are established. For specific classes of semigroups, such as bounded analytic or exponentially γ -stable ones, stronger estimates are proved. Finally, applications to the inversion of the vector-valued Laplace transform are given.

Mathematics Subject Classification (1991)

Primary 47D06 41A21 41A25 Secondary 44A10 65J08 

Keywords

Rational approximation Operator semigroup Functional calculus Padé approximant Inverse Laplace transform γ-boundedness 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands

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