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Proceedings of the American Mathematical Society

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

 

 

Unitary one-parameter groups with finite speed of propagation


Author: E. C. Svendsen
Journal: Proc. Amer. Math. Soc. 84 (1982), 357-361
MSC: Primary 58G11; Secondary 35L40, 47D10
MathSciNet review: 640230
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Abstract: Suppose that $ \xi $ is a Hermitian vector bundle over a Riemannian manifold and that $ U$ is a one-parameter group of linear operators on the set of smooth sections of $ \xi $ with compact support. We prove that if $ U$ satisfies a smoothness condition, is unitary, and propagates initial data with finite speed, then it can be constructed from the solutions of a first-order symmetric hyperbolic system of partial differential equations.


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DOI: https://doi.org/10.1090/S0002-9939-1982-0640230-6
Keywords: Symmetric hyperbolic system, finite speed of propagation, initial-value problem, unitary one-parameter group, Hermitian vector bundle
Article copyright: © Copyright 1982 American Mathematical Society