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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. 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 |
|---|---|
| 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 |
| ISSN: | 0143-3857 |
| Date: | October 2004 |
| Volume: | Vol.24 |
| Number: | No.5 |
| Page Range: | pp. 1277-1281 |
| Identification Number: | 10.1017/S0143385704000409 |
| Status: | Peer Reviewed |
| Access rights to Published version: | Open Access |
| References: | [1] 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. [2] M. R. Herman. Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations. Thesis, Orsay 1976. [3] K. E. Petersen. Introductory ergodic theory. Lecture Notes, University of North Carolina at Chapel Hill. [4] K. E. Petersen. On a series of cosecants related to a problem in ergodic theory. Compositio Math. 26 (1973), 313–317. [5] A. Zygmund. Trigonometric Series. Cambridge University Press, 1959. [6] A. Y. Gordon. Funktsional’ny Analiz Evo Prilozheniya 9(4) (1975), 71–72 (in Russian). |
| URI: | http://wrap.warwick.ac.uk/id/eprint/753 |
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