A new look at old theorems of Fejér and Hardy
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00582940" target="_blank" >RIV/67985840:_____/24:00582940 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s00025-023-02114-y" target="_blank" >https://doi.org/10.1007/s00025-023-02114-y</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00025-023-02114-y" target="_blank" >10.1007/s00025-023-02114-y</a>
Alternative languages
Result language
angličtina
Original language name
A new look at old theorems of Fejér and Hardy
Original language description
The article studies the convergence of trigonometric Fourier series via a new Tauberian theorem for Cesàro summable series in abstract normed spaces. This theorem generalizes some known results of Hardy and Littlewood for number series. We find sufficient conditions for the convergence of trigonometric Fourier series in homogeneous Banach spaces over the circle. These conditions are expressed in terms of the Fourier coefficients and are weaker than Hardy’s condition. We give a description of all Banach function spaces given over the circle and endowed with a norm been equivalent to a norm in a homogeneous Banach space. We study interpolation properties of such spaces and give new examples of them. We extend the classical Fejér theorem on the uniform Cesàro summability of the Fourier series on sets by means of a refined version of Cantor’s theorem on the uniform continuity of a mapping between metric spaces. We also generalize the classical Hardy theorem on the uniform convergence of the Fourier series on sets.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Results in Mathematics
ISSN
1422-6383
e-ISSN
1420-9012
Volume of the periodical
79
Issue of the periodical within the volume
2
Country of publishing house
DE - GERMANY
Number of pages
14
Pages from-to
88
UT code for WoS article
001162454900001
EID of the result in the Scopus database
2-s2.0-85184190902