Unitary groups and differential operators
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 as t approaches infinity provided that is a differential operator for all t and A has certain properties.
-  Seymour Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0200692
-  R. M. Kauffman, Operator theory of a class of ordinary differential expressions, J. Differential Equations (submitted).
-  Peter D. Lax and Ralph S. Phillips, Scattering theory, Pure and Applied Mathematics, Vol. 26, Academic Press, New York-London, 1967. MR 0217440
- S. Goldberg, Unbounded linear operators: Theory and applications, McGraw-Hill, New York, 1966. MR 34 #580. MR 0200692 (34:580)
- R. M. Kauffman, Operator theory of a class of ordinary differential expressions, J. Differential Equations (submitted).
- P. Lax and R. S. Phillips, Scattering theory, Pure and Appl. Math., vol. 26, Academic Press, New York, 1967. MR 36 #530. MR 0217440 (36:530)
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Keywords: Unitary group, differential operator, eigenvector
Article copyright: © Copyright 1971 American Mathematical Society