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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}.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1977 American Mathematical Society