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- W1489385824 abstract "Consider the function [ f(x)=sum _{n=0}^{+infty }b^{-n}g(b^nx)] where $b>1$ and $g$ is an almost periodic $C^{1,varepsilon }$ function. It is well known that the function $f$ lives in the so-called Zygmund class. We prove that $f$ is generically nowhere differentiable. This is the case in particular if the elementary condition $g^prime (0)not = 0$ is satisfied. We also give a sufficient condition on the Fourier coefficients of $g$ which ensures that $f$ is nowhere differentiable." @default.
- W1489385824 created "2016-06-24" @default.
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- W1489385824 date "2005-03-22" @default.
- W1489385824 modified "2023-09-23" @default.
- W1489385824 title "Weierstrass functions in Zygmund’s class" @default.
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- W1489385824 doi "https://doi.org/10.1090/s0002-9939-05-07857-3" @default.
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