L2 regularity of measurable solutions of a finite-difference equation of the circle
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. ISSN 0143-3857
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Official URL: http://dx.doi.org/10.1017/S0143385704000409
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|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of 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|
|Official Date:||October 2004|
|Page Range:||pp. 1277-1281|
|Access rights to Published version:||Open Access|
 D. V. Anosov. On an additive functional homology equation connected with an ergodic rotation of the circle. Translation Math. U.S.S.R. Izvestija 74 (1973), 1257–1271.
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