Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

On summability of Fourier series at a point
HTML articles powered by AMS MathViewer

by G. D. Dikshit PDF
Proc. Amer. Math. Soc. 92 (1984), 245-250 Request permission

Abstract:

In this paper summability of Fourier series by a regular linear method of summation determined by a triangular matrix, has been studied and various results—some known and some new—on Cesàro and Nörlund summability have been deduced. A convergence criterion has also been obtained.
References
  • G. D. Dikshit, A note on Riesz and Nörlund means, Rend. Circ. Mat. Palermo (2) 18 (1969), 49–61. MR 283454, DOI 10.1007/BF02888945
    • G. H. Hardy, On the summability of Fourier series, Proc. London Math. Soc. (2) 12 (1913), 365-372; also in Collected papers of G. H Hardy, Vol. 3, Oxford Univ. Press, 1969, pp. 118-125.
  • Godfrey Harold Hardy and John Edensor Littlewood, Some new convergence criteria for Fourier series, Ann. Scuola Norm. Super. Pisa Cl. Sci. (2) 3 (1934), no. 1, 43–62. MR 1556721
  • Leonard McFadden, Absolute Nörlund summability, Duke Math. J. 9 (1942), 168–207. MR 6379
  • T. Pati, A generalization of a theorem of Iyengar on the harmonic summability of Fourier series, Indian J. Math. 3 (1961), 85–90. MR 150530
  • J. A. Siddiqi, On the harmonic summability of Fourier series, Proc. Indian Acad. Sci., Sect. A. 28 (1948), 527–531. MR 0027878
  • Tarkeshwar Singh, On Nörlund summability of Fourier series and its conjugate series, Proc. Nat. Inst. Sci. India Part A 29 (1963), 65–73. MR 155142
  • T. Singh, Nörlund summability of Fourier series and its conjugate series, Ann. Mat. Pura Appl. (4) 64 (1964), 123–132. MR 166550, DOI 10.1007/BF02410051
  • Gen-ichiro Sunouchi, Convergence criteria for Fourier series, Tohoku Math. J. (2) 4 (1952), 187–193. MR 51955, DOI 10.2748/tmj/1178245421
  • A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC: 42A24
  • Retrieve articles in all journals with MSC: 42A24
Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 92 (1984), 245-250
  • MSC: Primary 42A24
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0754712-1
  • MathSciNet review: 754712