Computable analysis of the abstract Cauchy problem in a Banach space and its applications I
Klaus Weihrauch, Ning Zhong · Mathematical logic quarterly · 2007
Abstract We study computability of the abstract linear Cauchy problem equation image 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)