Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T06:21:03.409Z Has data issue: false hasContentIssue false

On the absolute summability factor of Fourier series

Published online by Cambridge University Press:  17 April 2009

Yasuo Okuyama
Affiliation:
Department of Mathematics, Faculty of Engineering, Shinshu University, Nagano 380, Japan.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The purpose of this paper is to give a general theorem on the absolute Riesz summability factor of Fourier series which implies Matsumoto's Theorem [Tôhoku Math. J. 8 (1956), 114–124] and to deduce some results from the theorem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1981

References

[1]Dikshit, G.D., “Localization relating to the summability |R, λn, 1| of Fourier series”, Indian J. Math. 7 (1965), 3139.Google Scholar
[2]Izumi, Masako and Izumi, Shin-ichi, “Absolute Nörlund summability factor of Fourier series”, Proc. Japan Acad. 46 (1970), 175188.Google Scholar
[3]Izumi, Masako and Izumi, Shin-ichi, “Absolute Norlund summability factor of Fourier series”, Indian J. Math. 12 (1970), 175188.Google Scholar
[4]Kolhekar, S.V., “On absolute Nörlund summabillty factors for Fourier series”, Ann. Polon. Math. 18 (1966), 107113.CrossRefGoogle Scholar
[5]Leindler, László, “On the absolute summability factors of Fourier series”, Acta sci. Math. 28 (1967), 323336.Google Scholar
[6]Matsumoto, Kishi, “Local property of the summability |R, λn, 1|”, Tôhoku Math. J. (2) 8 (1956), 114124.CrossRefGoogle Scholar
[7]Mohanty, R., “On the summability |R, log w, 1| of a Fourier series”, J. London Math. Soc. 25 (1950), 6772.CrossRefGoogle Scholar