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Estimates for the wave operator on the torus ${\Pi }^n$


Author: Akos Magyar
Journal: Proc. Amer. Math. Soc. 125 (1997), 1969-1976
MSC (1991): Primary 35L15; Secondary 11L07
DOI: https://doi.org/10.1090/S0002-9939-97-03676-9
MathSciNet review: 1363177
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Abstract: We prove $L^{p^{\prime }}\rightarrow L^p$ bounds for the wave operator on the torus for large time. The new feature is the distribution of the singularities of the wave kernel, which can be understood by making use of Hardy-Littlewood method for exponential sums.


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Additional Information

Akos Magyar
Affiliation: The Instittue for Advanced Study, Princeton, New Jersey 08540
Address at time of publication: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: amagyar@cco.caltech.edu

DOI: https://doi.org/10.1090/S0002-9939-97-03676-9
Received by editor(s): September 28, 1995
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 1997 American Mathematical Society