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

DOI:
https://doi.org/10.1090/S0002-9939-1982-0640230-6

MathSciNet review:
640230

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Abstract: Suppose that is a Hermitian vector bundle over a Riemannian manifold and that is a one-parameter group of linear operators on the set of smooth sections of with compact support. We prove that if 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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Additional Information

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