Kernel estimates and -spectral independence of generators of -semigroups |
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Authors: | Hisakazu Shindoh |
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Institution: | aDepartment of Mathematics, Faculty of Science, Tokyo University of Science, 26 Wakamiya-cho, Shinjuku-ku, Tokyo 162-0827, Japan |
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Abstract: | After the appearance of W. Arendt's result that “Gaussian estimate of a semigroup implies the Lp-spectral independence of the generator,” various generalizations have been obtained. This paper shows that a certain kernel estimate of a semigroup implies the Lp-spectral independence of the generator, generalizing the case of upper Gaussian estimate and “Gaussian estimate of order α (0,1] S. Miyajima, H. Shindoh, Gaussian estimates of order α and Lp-spectral independence of generators of C0-semigroups, Positivity 11 (1) (2007) 15–39], Definition 3.1.” The proof uses S. Karrmann's result about the Lp-spectral independence and B.A. Barnes' theorem about the spectrum of integral operators. As an application, the Lp-spectral independence of −(−Δ)α+V] (α (0,1]) for a suitable V is proved with the help of a recent result by V. Liskevich, H. Vogt and J. Voigt V. Liskevich, H. Vogt, J. Voigt, Gaussian bounds for propagators perturbed by potentials, J. Funct. Anal. 238 (2006) 245–277]. |
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Keywords: | color:black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6WJJ-4T0805C-1&_mathId=mml12&_user=10&_cdi=6880&_rdoc=8&_acct=C000069468&_version=1&_userid=6189383&md5=fa2a67115bb8cecaa1f7e9d197cb69be" title="Click to view the MathML source" Lp-spectrum" target="_blank">alt="Click to view the MathML source">Lp-spectrum Integral kernel Banach algebra Gaussian estimate Fractional powers of an operator Spectral mapping theorem Positive semigroup Perturbation |
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