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)


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].


Banach Space Linear Operator Rational Number Turing Machine Bounded Linear Operator 
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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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