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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Gaussian estimates and holomorphy of semigroups
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by El-Maati Ouhabaz PDF
Proc. Amer. Math. Soc. 123 (1995), 1465-1474 Request permission

Abstract:

We show that if a selfadjoint semigroup T on ${L^2}(\Omega )$ satisfies a Gaussian estimate $|T(t)f| \leq MG(bt)|f|,0 \leq t \leq 1,f \in {L^2}(\Omega )$ (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.
References
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • 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