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Beyond the First Main Theorem – When Is the Solution of a Linear Cauchy Problem Computable?

  • Klaus Weihrauch
  • Ning Zhong
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)

Abstract

We study computabilty of the abstract linear Cauchy problem

du(t)/dt = Au(t), t > 0, u(0) = x ∈ X

where A is a linear operator on a Banach space X. We give necessary and sufficient conditions for A such that the operator K:xu is computable. We consider continuous operators and more generally closed operators A. For studying computability we use the representation approach to Computable Analysis (TTE) [7, 1] which is consistent with the model used in [6].

Keywords

Banach Space Linear Operator Rational Number Turing Machine Bounded Linear Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Klaus Weihrauch
    • 1
  • Ning Zhong
    • 2
  1. 1.University of HagenHagenGermany
  2. 2.University of CincinnatiCincinnatiUSA

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