Random homeomorphisms and Fourier expansions -- the pointwise behaviour

DOI10.1007/BF02787549zbMATH Open1066.42007arXivmath/0511036MaRDI QIDQ1885593

Gady Kozma

Publication date: 11 November 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/math/0511036

zbMATH Keywords

Fourier expansionDirichlet kernelFourier seriessuperpositionrandom perturbationrandom change of variableDubins-Freedman random homeomorphism

Mathematics Subject Classification ID

Strong limit theorems (60F15) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Probabilistic methods for one variable harmonic analysis (42A61)

Cites Work

• Random homeomorphisms
• Random homeomorphisms and Fourier expansions
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Related Items (1)

Homeomorphic changes of variable and Fourier multipliers

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