Convergence of the Fourier Series of Lip 1 Functions with Respect to General Orthonormal Systems

Convergence of the Fourier Series of Lip 1 Functions with Respect to General Orthonormal Systems

We establish sufficient conditions that should be satisfied by functions of a general orthonormal system (ONS) { φ n ( x )} in order that the Fourier series in this system be convergent almost everywhere on [0 , 1] for any function from the class Lip 1 . It is shown that the obtained conditions are...

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Veröffentlicht in:Ukrainian mathematical journal 2017-09, Vol.69 (4), p.546-560
Hauptverfasser: Gogoladze, L., Tsagareishvili, V.
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Analysis
Applications of Mathematics
Convergence
Fourier series
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Zusammenfassung:We establish sufficient conditions that should be satisfied by functions of a general orthonormal system (ONS) { φ n ( x )} in order that the Fourier series in this system be convergent almost everywhere on [0 , 1] for any function from the class Lip 1 . It is shown that the obtained conditions are best possible in a certain sense.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-017-1381-z