Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-29T07:04:15.443Z Has data issue: false hasContentIssue false

On the absolute Nörlund summability factors of Fourier series

Published online by Cambridge University Press:  17 April 2009

Yasuo Okuyama
Affiliation:
Department of Technology, Shinshu University, Nagano, 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 object of this paper is to give a general theorem which implies Izumi's Theorem and Kanno's Theorem on the absolute Nörlund summability factors of Fourier series and deduce to several known and new results from the theorem.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Bosanquet, L.S., “The absolute Cesàro summability of a Fourier series”, Proc. London Math. Soc. (2) 41 (1936), 517528.Google Scholar
[2]Dikshit, H.P., “Absolute summability of a Fourier series with factors”, preprint.Google Scholar
[3]Izumi, Masako and Izumi, Shin-Ichi, “Absolute Nörlund summability factor of Fourier series”, Proc. Japan Acad. 46 (1970), 642646.Google Scholar
[4]Kanno, Kōsi, “On the absolute Nörlund summability of the factored Fourier series”, Tôhoku Math. J. 21 (1969), 434447.Google Scholar
[5]McFadden, Leonard, “Absolute Nörlund summability”, Duke Math. J. 9 (1942), 168207.CrossRefGoogle Scholar
[6]Mohanty, R., “The absolute Cesàro summability of some series associated with a Fourier series and its allied series”, J. London Math. Soc. 25 (1950), 6367.CrossRefGoogle Scholar
[7]Mohanty, R., “Absolute Cesàro summability of a series associated with a Fourier series”, Bull. Calcutta Math. Soc. 44 (1952), 152154.Google Scholar
[8]Varshney, O.P., “On the absolute harmonic summability of a series related to a Fourier series”, Proc. Amer. Math. Soc. 10 (1959), 784789.Google Scholar