Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T13:28:24.109Z Has data issue: false hasContentIssue false
  • English
  • Français

Absolute summability of a fourier series and its derived series by a product method

Published online by Cambridge University Press:  09 April 2009

H. P. Dikshit
H. P. Dikshit
Affiliation:
Department of Post-Graduate Studies and Research in MathematicsUniversity of JabalpurJabalpur (India)
Rights & Permissions [Opens in a new window]

Extract

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.

Let Σan be a given infinite series with the sequence of partial sums {Sn}. Let {Pn} be a sequence of constants, real or complex, and let us write Pn = p0 + p1 + … + pn; P-1 = P-1 = 0.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 14 , Issue 4 , December 1972 , pp. 470 - 481
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Astrachan, Max, ‘Studies in the summability of Fourier series by Nörlund means’, Duke Math. J. 2 (1936), 543–569.CrossRefGoogle Scholar
[2]Bosanquet, L. S., ‘The absolute Cesàro summability of a Fourier series’, Proc. London. Math. Soc. 41 (1936), 517–528.CrossRefGoogle Scholar
[3]Dikshit, H. P., ‘Absolute summability of a Fourier series by Nörlund means’, Math. Z. 102 (1967), 166–170.CrossRefGoogle Scholar
[4]Dikshit, H. P., ‘A note on a theorem of Astrachan on the (N, pn) (C, 1) summability of a Fourier series’, Math. Student 33 (1964), 71–79.Google Scholar
[5]Dikshit, H. P., ‘On the absolute Nörlund summability of a Fourier series and its conjugate series’, Ködai Math. Sem. Rep. 20 (1968), 448–453.Google Scholar
[6]Hille, E. and Tamarkin, J. D., ‘On the summability of Fourier series I’, Trans. Amer. Math. Soc. 34 (1932), 757–783.CrossRefGoogle Scholar
[7]Hyslop, J. M., ‘On the absolute summability of the successively derived series of Fourier series and its allied series’, Proc. London Math. Soc. 46 (1940), 55–80.CrossRefGoogle Scholar
[8]Kogbetliantz, E., ‘Sur les séries absolument sommable par la méthode des moyennes arithmétique’, Bull. des Sc. Math. 49 (1925), 234–256.Google Scholar
[9]Kwee, B., ‘Absolute regularity of the Nörlund means’, J. Aust. Math. Soc. 5 (1965), 1–7.CrossRefGoogle Scholar
[10]Mears, F. M., ‘Some multiplication theorems for the Nörlund means,’ Bull. Amer. Math. Soc. 41 (1935), 875–880.CrossRefGoogle Scholar
[11]Nörlund, N. E., ‘Sur une application des fonctions permutables,’ Lunds Univ. Årss., 16 (1919), No. 3.Google Scholar
[12]Pati, T., ‘On the absolute Nörlund summability of a Fourier series,’ J. London. Math. Soc. 34 (1959), 153–160; Addendum: J. London Math. Soc. 37 (1962), 256.CrossRefGoogle Scholar
[13]Pati, T., ‘On the absolute summability of a Fourier series by Nörlund means,’ Math. Z. 88 (1965), 244–249.CrossRefGoogle Scholar
[14]Si-Lei, W., ‘On the absolute Nörlund summability of a Fourier series and its conjugate series’, Acta Math. Sinica 15 (1965), 281–295.Google Scholar
[15]Varshney, O. P., ‘On the absolute Nörlund summability of a Fourier series’, Math. Z. 83 (1964), 18–24.CrossRefGoogle Scholar