Abstract

Recently, it has been revealed that the semigroups satisfying Gaussian estimates inherit some of the nice properties enjoyed by the Gaussian semigroup itself. Arendt [1] gives a result in this direction, by proving the invariance of the spectrum of the generators of consistent C0-semigroups with Gaussian estimates. In this paper, we generalize this result to the semigroups estimated by the one generated by the fractional power –(I−Δ)α(12<α≤1).

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