Boundary values of holomorphic semigroups
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- by Khristo Boyadzhiev and Ralph deLaubenfels PDF
- Proc. Amer. Math. Soc. 118 (1993), 113-118 Request permission
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 $O(1 + |s{|^r})\;\forall r > \gamma \geqslant 0$, if and only if $||{e^{zA}}||$ is $O({((1 + |z|)/\operatorname {Re} (z))^r})\forall r > \gamma$ and $iA$ generates a bounded ${(1 - A)^{ - r}}$ regularized group $\forall r > \gamma \geqslant 0$ if and only if $||{e^{zA}}||$ is $O({(1/\operatorname {Re} (z))^r})\;\forall r > \gamma$. We apply this to the Schrödinger operator $i(\Delta - V)$.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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