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

Weihrauch Klaus | Zendy; Zhong Ning | Zendy

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

Author(s) -

Weihrauch Klaus,

Zhong Ning

Publication year - 2007

Publication title -

mathematical logic quarterly

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.473

H-Index - 28

eISSN - 1521-3870

pISSN - 0942-5616

DOI - 10.1002/malq.200710015

Subject(s) - computable analysis , computability , mathematics , banach space , cauchy problem , pure mathematics , cauchy distribution , computable number , cauchy sequence , operator (biology) , initial value problem , computable function , discrete mathematics , algebra over a field , mathematical analysis , biochemistry , chemistry , repressor , transcription factor , gene

We study computability of the abstract linear Cauchy problem (1)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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