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On summability of Fourier series at a point


Author: G. D. Dikshit
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
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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.


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  • [1] G. D. Dikshit, A note on Riesz and Nörlund means, Rend. Circ. Mat. Palermo (2) 18 (1969), 49-61. MR 0283454 (44:685)
  • [2] 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.
  • [3] G. H. Hardy and J. E. Littlewood, Some new convergence criteria for Fourier series, Ann. Scuola Norm. Sup. Pisa (2) 3 (1934), 43-62; also in Collected papers of G. H. Hardy, op. cit., pp. 68-88. MR 1556721
  • [4] L. McFadden, Absolute Nörlund summability, Duke Math. J. 9 (1942), 168-207. MR 0006379 (3:295g)
  • [5] T. Pati, A generalisation of a theorem of Iyengar on the harmonic summability of Fourier series, Indian J. Math. 3 (1961), 85-90. MR 0150530 (27:527)
  • [6] J. A. Siddiqi, On the harmonic summability of Fourier series, Proc. Nat. Acad. Sci. India Sect. A 28 (1948), 527-531. MR 0027878 (10:369a)
  • [7] T. Singh, On Nörlund summability of Fourier series and its conjugate series, Proc. Nat. Inst. Sci. India Part A 29 (1963), 65-73. MR 0155142 (27:5082)
  • [8] -, Nörlund summability of Fourier series and its conjugate series, Ann. Mat. Pura Appl. (4) 64 (1964), 123-132. MR 0166550 (29:3824)
  • [9] G. Sunouchi, Convergence criteria for Fourier series, Tôhoku Math. J. (2) 4 (1952), 187-193. MR 0051955 (14:552f)
  • [10] A. Zygmund, Trigonometric series, Vol. 1, Cambridge Univ. Press, 1968. MR 0236587 (38:4882)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0754712-1
Keywords: Triangular matrices, Cesàro method, Nörlund method, convergence criteria for Fourier series
Article copyright: © Copyright 1984 American Mathematical Society

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