Function classes and convergence almost everywhere

Function classes and convergence almost everywhere

For a certain class of orthonormal systems (ONS) on [0, 1] there exists a family of functions from L 2(0, 1), independent from that class, such that the Fourier series with respect to each ONS of the class converges a.e. for any member of the family. Similar result holds for the summability of Fouri...

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Veröffentlicht in:Georgian mathematical journal 2011-03, Vol.18 (1), p.177-189
1. Verfasser: Tsagareishvili, Vakhtang
Format: Artikel
Sprache:eng
Schlagworte:
Fourier series
modulus of continuity
Orthonormal system
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Beschreibung
Zusammenfassung:For a certain class of orthonormal systems (ONS) on [0, 1] there exists a family of functions from L 2(0, 1), independent from that class, such that the Fourier series with respect to each ONS of the class converges a.e. for any member of the family. Similar result holds for the summability of Fourier integrals.
ISSN:1072-947X
1072-9176
1572-9176
DOI:10.1515/gmj.2011.0008