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Proceedings of the American Mathematical Society

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



Unitary groups and differential operators

Author: Robert M. Kauffman
Journal: Proc. Amer. Math. Soc. 30 (1971), 102-106
MSC: Primary 47.60
MathSciNet review: 0282254
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Abstract: Unitary groups generated by differential operators have special properties that can be used to study completeness of the set of eigenvectors of the infinitesimal generator.

Unitary groups also occur in differential operator theory in another manner, associated with unitary equivalence of differential operators. We discuss what happens to $ {A_t} = U_t^{ - 1}A{U_t}$ as t approaches infinity provided that $ {A_t}$ is a differential operator for all t and A has certain properties.

References [Enhancements On Off] (What's this?)

  • [1] Seymour Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0200692
  • [2] R. M. Kauffman, Operator theory of a class of ordinary differential expressions, J. Differential Equations (submitted).
  • [3] Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440

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Keywords: Unitary group, differential operator, eigenvector
Article copyright: © Copyright 1971 American Mathematical Society