Advertisement
Published in:
2006 | OriginalPaper | Chapter
Beyond the First Main Theorem – When Is the Solution of a Linear Cauchy Problem Computable?
Authors : Klaus Weihrauch, Ning Zhong
Published in: Theory and Applications of Models of Computation
Publisher: Springer Berlin Heidelberg
Activate our intelligent search to find suitable subject content or patents.
Select sections of text to find matching patents with Artificial Intelligence. powered by
Select sections of text to find additional relevant content using AI-assisted search. powered by
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
:
x
↦
u
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].