L2 regularity of measurable solutions of a finite-difference equation of the circle
Published online by Cambridge University Press: 18 October 2004
Extract
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.
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- © 2004 Cambridge University Press
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