Random homeomorphisms and Fourier expansions - the pointwise behavior
Classical Analysis and ODEs
2007-05-23 v1 Probability
Abstract
Let phi be a Dubins-Freedman random homeomorphism on [0,1] derived from the base measure uniform on the vertical line x=1/2, and let f be a periodic function satisfying that |f(x)-f(0)| = o(1/log log log 1/x). Then the Fourier expansion of f composed with phi converges at 0 with probability 1. In the condition on f, o cannot be replaced by O. Also we deduce some 0-1 laws for this kind of problems.
Cite
@article{arxiv.math/0511036,
title = {Random homeomorphisms and Fourier expansions - the pointwise behavior},
author = {Gady Kozma},
journal= {arXiv preprint arXiv:math/0511036},
year = {2007}
}
Comments
20 pages. Part of my PhD thesis