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L2 regularity of measurable solutions of a finite-difference equation of the circle
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Herman, Michael R. (2004) L2 regularity of measurable solutions of a finite-difference equation of the circle. Ergodic Theory and Dynamical Systems, Vol.24 (No.5). pp. 1277-1281. doi:10.1017/S0143385704000409 ISSN 0143-3857.
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Official URL: http://dx.doi.org/10.1017/S0143385704000409
Abstract
We show that if $\varphi$ is a lacunary Fourier series and the equation $\psi (x) -\psi (x + \alpha) = \varphi(x), x \bmod 1$ has a measurable solution $\varphi$, then in fact the equation has a solution in L2.
This work of Michel Herman (1942-2000) appeared only as a preprint of the Mathematics Institute, University of Warwick, dated May 1976. It was turned into TEX format by Claire Desescures. Minor editorial work was done by Albert Fathi.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Library of Congress Subject Headings (LCSH): | Fourier series, Differential equations, Calculas, Circle, Curves, Algebraic | ||||
Journal or Publication Title: | Ergodic Theory and Dynamical Systems | ||||
Publisher: | Cambridge University Press | ||||
ISSN: | 0143-3857 | ||||
Official Date: | October 2004 | ||||
Dates: |
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Volume: | Vol.24 | ||||
Number: | No.5 | ||||
Page Range: | pp. 1277-1281 | ||||
DOI: | 10.1017/S0143385704000409 | ||||
Status: | Peer Reviewed | ||||
Access rights to Published version: | Open Access (Creative Commons) |
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