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Boundary values of holomorphic semigroups


Authors: Khristo Boyadzhiev and Ralph deLaubenfels
Journal: Proc. Amer. Math. Soc. 118 (1993), 113-118
MSC: Primary 47D03; Secondary 35J10, 47F05
DOI: https://doi.org/10.1090/S0002-9939-1993-1128725-X
MathSciNet review: 1128725
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Abstract: Suppose $ A$ generates a bounded strongly continuous holomorphic semigroup of angle $ \pi /2$. We show that $ iA$ generates a $ {(1 - A)^{ - r}}$ regularized group, which is $ O(1 + \vert s{\vert^r})\;\forall r > \gamma \geqslant 0$, if and only if $ \vert\vert{e^{zA}}\vert\vert$ is $ O({((1 + \vert z\vert)/\operatorname{Re} (z))^r})\forall r > \gamma $ and $ iA$ generates a bounded $ {(1 - A)^{ - r}}$ regularized group $ \forall r > \gamma \geqslant 0$ if and only if $ \vert\vert{e^{zA}}\vert\vert$ is $ O({(1/\operatorname{Re} (z))^r})\;\forall r > \gamma $. We apply this to the Schrödinger operator $ i(\Delta - V)$.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1128725-X
Article copyright: © Copyright 1993 American Mathematical Society

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