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## L2 regularity of measurable solutions of a finite-difference equation of the circle

### 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.\ud \ud 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

Topics: QA
Publisher: Cambridge University Press
Year: 2004
OAI identifier: oai:wrap.warwick.ac.uk:753

### Citations

1. (1975). Funktsional’ny Analiz Evo Prilozheniya
2. Introductory ergodic theory. Lecture Notes,
3. (1973). On an additive functional homology equation connected with an ergodic rotation of the circle.
4. (1973). Ona series ofcosecants related to a problem in ergodic theory.
5. (1976). Sur la conjugaison diff´ erentiable des diff´ eomorphismes du cercle ` a des rotations. Thesis,
6. (1959). Trigonometric Series.

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