Results on spline-Fourier and Ciesielski-Fourier series

Ferenc Weisz

Banach Center Publications (2006)

  • Volume: 72, Issue: 1, page 367-383
  • ISSN: 0137-6934

Abstract

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Some recent results on spline-Fourier and Ciesielski-Fourier series are summarized. The convergence of spline Fourier series and the basis properties of the spline systems are considered. Some classical topics, that are well known for trigonometric and Walsh-Fourier series, are investigated for Ciesielski-Fourier series, such as inequalities for the Fourier coefficients, convergence a.e. and in norm, Fejér and θ-summability, strong summability and multipliers. The connection between Fourier series and Hardy spaces is studied.

How to cite

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Ferenc Weisz. "Results on spline-Fourier and Ciesielski-Fourier series." Banach Center Publications 72.1 (2006): 367-383. <http://eudml.org/doc/282275>.

@article{FerencWeisz2006,
abstract = {Some recent results on spline-Fourier and Ciesielski-Fourier series are summarized. The convergence of spline Fourier series and the basis properties of the spline systems are considered. Some classical topics, that are well known for trigonometric and Walsh-Fourier series, are investigated for Ciesielski-Fourier series, such as inequalities for the Fourier coefficients, convergence a.e. and in norm, Fejér and θ-summability, strong summability and multipliers. The connection between Fourier series and Hardy spaces is studied.},
author = {Ferenc Weisz},
journal = {Banach Center Publications},
keywords = {Hardy spaces; -atoms; spline and Ciesielski systems; Walsh system; Hardy–Littlewood and Paley type inequalities; Fejér means; strong summability; multipliers; Sunouchi operator},
language = {eng},
number = {1},
pages = {367-383},
title = {Results on spline-Fourier and Ciesielski-Fourier series},
url = {http://eudml.org/doc/282275},
volume = {72},
year = {2006},
}

TY - JOUR
AU - Ferenc Weisz
TI - Results on spline-Fourier and Ciesielski-Fourier series
JO - Banach Center Publications
PY - 2006
VL - 72
IS - 1
SP - 367
EP - 383
AB - Some recent results on spline-Fourier and Ciesielski-Fourier series are summarized. The convergence of spline Fourier series and the basis properties of the spline systems are considered. Some classical topics, that are well known for trigonometric and Walsh-Fourier series, are investigated for Ciesielski-Fourier series, such as inequalities for the Fourier coefficients, convergence a.e. and in norm, Fejér and θ-summability, strong summability and multipliers. The connection between Fourier series and Hardy spaces is studied.
LA - eng
KW - Hardy spaces; -atoms; spline and Ciesielski systems; Walsh system; Hardy–Littlewood and Paley type inequalities; Fejér means; strong summability; multipliers; Sunouchi operator
UR - http://eudml.org/doc/282275
ER -

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