 | Cím: Speciális de la Vallée Poussin-féle Vilenkin-Fourier közepek majdnem mindenütti konvergenciája Szerző: Blahota István - Nagy Dóra Kiadó neve: Nyíregyházi Egyetem, Matematika és Informatika Intézet DOI: https://doi.org/10.71066/VARECZA.2025.1.01 Megjelenés: 2025. december Letöltés / Megtekintés (PDF): letöltés |
Összefoglaló:
Korlátos Vilenkin–Fourier-rendszereken vizsgálunk egy de la Vallée Poussin-típusú mátrix-transzformációs
összegzési eljárást. Megadjuk azokat a monotonitási és egyéb feltételeket a súlyokra, amelyek biztosítják,
hogy az így kapott közepek majdnem mindenütt tartsanak az eredeti függvényhez minden integrálható függvény
esetén.
Kulcsszavak:
Fourier-sor, Vilenkin-rendszer, majdnem mindenütti konvergencia, mátrix-transzformációs közép.
Abstract:
We investigate a de la Vallée Poussin-type matrix transformation summation procedure on bounded Vilenkin-
Fourier systems. We give the monotonicity and other conditions on the weights that ensure that the resulting
means converge to the original function almost everywhere, for every integrable function.
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