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A strong contractivity property for semigroups generated by differential operators

Author: Robert M. Kauffman
Journal: Trans. Amer. Math. Soc. 307 (1988), 153-169
MSC: Primary 47F05; Secondary 35B40, 35K10, 47D05
MathSciNet review: 936810
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Abstract: Frequently, nonconservative semigroups generated by partial differential operators in $ {L_{2,\rho }}({R^k})$ have the property that initial conditions which are large at $ \vert x\vert = \infty $ become immediately small at infinity for all $ t > 0$. This property is related to the rate of decay of eigenfunctions of the differential operator. In this paper this phenomenon is investigated for a large class of differential operators of second and higher order. New estimates on the rate of decay of the eigenfunctions are included, which are related in special cases to those of Agmon.

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Article copyright: © Copyright 1988 American Mathematical Society

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