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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A strong contractivity property for semigroups generated by differential operators
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by Robert M. Kauffman PDF
Trans. Amer. Math. Soc. 307 (1988), 153-169 Request permission

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 $|x| = \infty$ 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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 307 (1988), 153-169
  • MSC: Primary 47F05; Secondary 35B40, 35K10, 47D05
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0936810-0
  • MathSciNet review: 936810