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Computable analysis of the abstract Cauchy problem in a Banach space and its applications I

✍ Scribed by Klaus Weihrauch; Ning Zhong

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 222 KB
Volume: 53
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200710015

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We study computability of the abstract linear Cauchy problem

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where A is a linear operator, possibly unbounded, on a Banach space X. We give necessary and sufficient conditions for A such that the solution operator K: x ↦ u of the problem (1) is computable. For studying computability we use the representation approach to computable analysis developed by Weihrauch and others. This approach is consistent with the model used by Pour‐El/Richards. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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