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TIME AVERAGES FOR THE LAPLACE GROUP
Published online by Cambridge University Press: 15 February 2005
Abstract
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The imaginary powers of the Laplace operator over the circle give a $C_0$ group of bounded linear operators on $\mathsf{L}_{\theta}^p(0,2\pi)$ ($1\ltp\lt\infty$). Whereas the group is unbounded on $\mathsf{L}^4$, this paper shows that the $\mathsf{L}^4$ long-time averages of each $f$ in $\mathsf{L}^2$ are bounded. This is a Fourier restriction phenomenon.
AMS 2000 Mathematics subject classification: Primary 42A15; 42B15
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 48 , Issue 1 , February 2005 , pp. 143 - 149
- Copyright
- Copyright © Edinburgh Mathematical Society 2005
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