A uniqueness theorem for orthonormal spline series

A uniqueness theorem for orthonormal spline series

We obtain recovery formulas for coefficients of orthonormal spline series by means of its sum, if the partial sums of an orthonormal spline series converge in measure to a function and the majorant of partial sums satisfies some necessary condition, provided that the spline system corresponds to a “...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Acta mathematica Hungarica 2024-10, Vol.174 (1), p.20-48
Hauptverfasser: Keryan, K. A., Khachatryan, A. L.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Uniqueness theorems
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We obtain recovery formulas for coefficients of orthonormal spline series by means of its sum, if the partial sums of an orthonormal spline series converge in measure to a function and the majorant of partial sums satisfies some necessary condition, provided that the spline system corresponds to a “regular” sequence. Additionally, it is proved that the regularity of the sequence is essential.
ISSN:0236-5294
1588-2632
DOI:10.1007/s10474-024-01472-5