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Gaussian estimates and holomorphy of semigroups


Author: El-Maati Ouhabaz
Journal: Proc. Amer. Math. Soc. 123 (1995), 1465-1474
MSC: Primary 47D06; Secondary 47F05, 47N20
DOI: https://doi.org/10.1090/S0002-9939-1995-1232142-3
MathSciNet review: 1232142
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Abstract: We show that if a selfadjoint semigroup T on $ {L^2}(\Omega )$ satisfies a Gaussian estimate $ \vert T(t)f\vert \leq MG(bt)\vert f\vert,0 \leq t \leq 1,f \in {L^2}(\Omega )$ (where $ G = G{(t)_{t \geq 0}}$ is the Gaussian semigroup on $ {L^2}({R^N})$ and $ \Omega $ is an open set of $ {R^N}$), then T defines a holomorphic semigroup of angle $ \frac{\pi }{2}$ on $ {L^p}(\Omega )$ . We obtain by duality the same result on $ {C_0}(\Omega )$. Applications to uniformly elliptic operators and Schrödinger operators are given.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1232142-3
Article copyright: © Copyright 1995 American Mathematical Society

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