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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the absence of necessary conditions for linear evolution operators


Author: Jerome A. Goldstein
Journal: Proc. Amer. Math. Soc. 64 (1977), 77-80
MSC: Primary 47D05; Secondary 34G05
MathSciNet review: 0500284
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Abstract: There exist selfadjoint operators $ A(t)(t \geqslant 0)$, whose resolvents depend smoothly on t, such that the initial value (Schrödinger) problem $ du(t)/dt = iA(t)u(t),u(0) = f$ has a unique $ ({C^\infty })$ solution u for each f in a dense set in the underlying Hilbert space, with u depending continuously on f, and yet the intersection over $ t \geqslant 0$ of the domain of $ A(t)$ is {0}.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0500284-2
PII: S 0002-9939(1977)0500284-2
Article copyright: © Copyright 1977 American Mathematical Society