Universally divergent Fourier series via Landau's extremal functions

Gerd Herzog; Peer Chr. Kunstmann

Commentationes Mathematicae Universitatis Carolinae (2015)

  • Volume: 56, Issue: 2, page 159-168
  • ISSN: 0010-2628

Abstract

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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 } .

How to cite

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Herzog, Gerd, and Kunstmann, Peer Chr.. "Universally divergent Fourier series via Landau's extremal functions." Commentationes Mathematicae Universitatis Carolinae 56.2 (2015): 159-168. <http://eudml.org/doc/270134>.

@article{Herzog2015,
abstract = {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 \lbrace 1\rbrace $.},
author = {Herzog, Gerd, Kunstmann, Peer Chr.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Fourier series; universal functions; Landau's extremal functions; Fourier series; universal functions; Landau's extremal functions},
language = {eng},
number = {2},
pages = {159-168},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Universally divergent Fourier series via Landau's extremal functions},
url = {http://eudml.org/doc/270134},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Herzog, Gerd
AU - Kunstmann, Peer Chr.
TI - Universally divergent Fourier series via Landau's extremal functions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 2
SP - 159
EP - 168
AB - 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 \lbrace 1\rbrace $.
LA - eng
KW - Fourier series; universal functions; Landau's extremal functions; Fourier series; universal functions; Landau's extremal functions
UR - http://eudml.org/doc/270134
ER -

References

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