Convergence of subdiagonal Padé approximations of C0-semigroups
Résumé
Let (rn)n∈N be the sequence of subdiagonal Padé approximations of the exponential function. We prove that for −A the generator of a uniformly bounded C0-semigroup T on a Banach space X, the sequence (rn(−tA))n∈N converges strongly to T(t) on D(Aα) for 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.
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