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- Publisher
- Springer Journals
- Copyright
- Copyright © 2013 by Springer Basel
- Subject
- Mathematics; Analysis
- ISSN
- 1424-3199
- eISSN
- 1424-3202
- DOI
- 10.1007/s00028-013-0207-1
- Publisher site
- See Article on Publisher Site
Abstract
Let $${(r_{n})_{n \in \mathbb{N}}}$$ ( r n ) n ∈ 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 $${(r_{n}(-t A))_{n \in \mathbb{N}}}$$ ( r n ( - t A ) ) n ∈ N converges strongly to T ( t ) on D( A α ) for $${\alpha>\frac{1}{2}}$$ α > 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.
Journal
Journal of Evolution Equations – Springer Journals
Published: Dec 1, 2013