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Keywords:
Fourier series; universal functions; Landau's extremal functions
Fourier series; universal functions; Landau's extremal functions
Summary:
We prove the existence of functions $f\in A(\mathbb D)$, the Fourier series of which being universally divergent on countable subsets of $\mathbb T = \partial \mathbb D$. The proof is based on a uniform estimate of the Taylor polynomials of Landau's extremal functions on $\mathbb T\setminus\{1\}$.
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