"Rational approximations of semigroups without scaling and squaring" by Frank Neubrander, Koray Ozer et al.
 

Rational approximations of semigroups without scaling and squaring

Document Type

Article

Publication Title

Discrete and Continuous Dynamical Systems- Series A

Publication Date

11-1-2013

Abstract

We show that for all q ≥ 1 and 1 ≤ i ≤ q there exist pairwise conjugate complex numbers bq;i and q;i with Re(q;i) > 0 such that for any generator (A;D(A)) of a bounded, strongly continuous semigroup T(t) on Banach space X with resolvent R(A) := (I A)-1 the expression bq;1 t R( q;1 t ;A) + bq;2 t R( q;2 t ;A) + + bq;q t R( q;q t ;A) provides an excellent approximation of the semigroup T(t) on D(A2q-1). Precise error estimates as well as applications to the numerical inversion of the Laplace transform are given.

Volume

33

Issue

11-12

First Page

5305

Last Page

5317

DOI

10.3934/dcds.2013.33.5305

ISSN

10780947

E-ISSN

15535231

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