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Universally divergent Fourier series via Landau's extremal functions

Gerd Herzog, Peer Chr. Kunstmann (2015)

Commentationes Mathematicae Universitatis Carolinae

We prove the existence of functions f A ( 𝔻 ) , the Fourier series of which being universally divergent on countable subsets of 𝕋 = 𝔻 . The proof is based on a uniform estimate of the Taylor polynomials of Landau’s extremal functions on 𝕋 { 1 } .

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