Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-1982-0640230-6
MathSciNet review: 640230
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


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

  • [1] S. J. Berman, Wave equations with finite velocity of propagation, Trans. Amer. Math. Soc. 188 (1974), 127-148. MR 0330781 (48:9118)
  • [2] P. R. Chernoff, Essential self-adjointness of powers of generators of hyperbolic equations, J. Funct. Anal. 12 (1973), 401-414. MR 0369890 (51:6119)
  • [3] I. M. Gel'fand and G. E. Šilov, Fourier transforms of rapidly increasing functions and questions of the uniqueness of the solution of Cauchy's problem, Amer. Math. Soc. Transl. (2) 5 (1957), 221-274. MR 0083624 (18:736a)
  • [4] S. Helgason, Differential geometry and symmetric spaces, Academic Press, New York, 1962. MR 0145455 (26:2986)
  • [5] J. Peetre, Rectifications à l'article "Une caractérisation abstraite des opérateurs différentiels", Math. Scand. 8 (1960), 116-120. MR 0124611 (23:A1923)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58G11, 35L40, 47D10

Retrieve articles in all journals with MSC: 58G11, 35L40, 47D10


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

American Mathematical Society