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A study of the matrix method of summability of the trigonometrical series

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References

  1. L. S. Bosanquet,On the Cesáro summation of Fourier series and allied series, Proc. London Math. Soc., vol. 37 (1934), pp. 17–32.

    Article  MATH  Google Scholar 

  2. H. C. Chow,Cesàro means connected with the allied series of a Fourier series, Jour. Chinese Math. Soc., 2 (1940), pp. 291–300.

    Google Scholar 

  3. R. G. Cooke,Infinite Matrices and sequence spaces, Macmillan, (1950).

  4. L. Fejér,Über die Bestimmung des sprunges der Funktion aus ihrer Fourierreihe, J. reine angew Math., 142 (1913), pp. 165–168.

    Google Scholar 

  5. N. K. Govil,On the summability of a class of Fourier series, Math. Student, 31 (1963), pp. 7–12.

    MATH  MathSciNet  Google Scholar 

  6. F. C. Hsiang,On the Riesz summability of Fourier series, Proc. American Math. Soc., 9 (1958), pp. 37–44.

    Article  MATH  MathSciNet  Google Scholar 

  7. F. C. Hsiang,On some extension of theorem of Fejér, Math. Scand., 7 (1959), pp. 333–336.

    MATH  MathSciNet  Google Scholar 

  8. F. C. Hsiang,On a theorem of Fejér, Pacific Jour. Math., 11 (1961), pp. 1359–1362.

    MATH  MathSciNet  Google Scholar 

  9. W. Jurkat,Zur convergenztheorie der Fourier-Riehen, Math. Zeit., 53 (1950), pp. 309–339.

    Article  MATH  MathSciNet  Google Scholar 

  10. G. G. Lorentz,A contribution to the theory of divergent series, Acta Math., 80 (1948), pp. 167–190.

    Article  MathSciNet  Google Scholar 

  11. G. G. Lorentz,Direct theorems on methods of summability, Canad. J. Math., 11 (1949), pp. 305–319.

    MathSciNet  Google Scholar 

  12. W. G. Morgan,On the convergence criteria of Hardy and Littlewood for Fourier series, Annali della Scuola Normale Superiore di Pisa, 4 (1935), pp. 337–382.

    Google Scholar 

  13. R. Mohanti and M. Nanda,On the behaviour of Fourier coefficients, Proc. Amer. Math. Soc., 5 (1954), pp. 79–84.

    Article  MathSciNet  Google Scholar 

  14. G. M. Petersen,Summability of a class of Fourier series, Proc. Amer. Math. Soc., 11 (1960), pp. 994–998.

    Article  MathSciNet  Google Scholar 

  15. O. P. Rai,Thesis presented for the degree of Ph. D. of Saugar University (1966), chap. VI.

  16. C. T. Rajagopal,Convergence and summability of a class of Fourier series, Indian Jour. Math., 3 (1961), pp. 63–72.

    MATH  MathSciNet  Google Scholar 

  17. G. Sansone,Orthogonal Functions, (New York, 1959).

  18. P. L. Sharma,On the sequence of Fourier coefficients, Proc. Amer. Math. Soc. 15 (3) (1964), pp. 337–340.

    Article  MATH  MathSciNet  Google Scholar 

  19. P. L. Sharma,On the sequence of Fourier coefficients, Proc. Japan Acad., 41 (1) (1965), pp. 52–55.

    Article  MATH  MathSciNet  Google Scholar 

  20. J. A. Siddiqi,On a theorem of Fejér, Math. Zeitschr, 61 (1954), pp. 79–81.

    Article  MATH  MathSciNet  Google Scholar 

  21. J. A. Siddiqi,The Fourier coefficients of continuous functions of bounded variation Math. Annalen, 143 (1961), pp. 103–108.

    Article  MATH  MathSciNet  Google Scholar 

  22. G. Sunouchi,Notes on the Fourier series I, On the convergence test of Fourier series, Mathematica Japanica, I (1948–49), pp. 41–44.

    MathSciNet  Google Scholar 

  23. G. Sunouchi and S. Izumi,Notes on Fourier Analysis (XXXIX): Theorems concerning Cesàro Summability, Tôhoku Math. Jour. (second series), 1 (3) (1951), pp. 313–326.

    MathSciNet  Google Scholar 

  24. Otto Szasz,On the Logorithmic means of Rearranged partial sums of a Fourier series, Bull. Amer. Math. Soc. (Part II), 48 (1942), pp. 705–711.

    MATH  MathSciNet  Google Scholar 

  25. Otto Szasz,On some Trigonometric Summability methods and Gibb’s phenomenon, Trans. Amer. Math. Soc., 54 (1943), pp. 483–497.

    Article  MATH  MathSciNet  Google Scholar 

  26. E. C. Titchmarsh,Theory of functions, p. 440 (1952).

  27. M. Tomic,The summability of a class of Fourier series, Acad. Serbe Sci. Arts Glas Cl. Sci. Math Nat., 254 (1963), pp. 25–34.

    MathSciNet  Google Scholar 

  28. O. P. Varshney,On the sequence of Fourier coefficients, Proc. Amer. Math. Soc., 10 (1959), pp. 790–795.

    Article  MATH  MathSciNet  Google Scholar 

  29. F. T. Wang,A remark on the c summability of Fourier series, Jour. Lond. Math. Soc., vol. 21–22, (1946–47), pp. 40–47.

    Google Scholar 

  30. F. T. Wang,On the Riesz summability of Fourier series, Proc. London Math. Soc., 47 (1942), pp. 308–325.

    Article  MATH  MathSciNet  Google Scholar 

  31. F. T. Wang,On the Riesz summability of Fourier series, III, Proc. London Math. Soc., 51 (1949), pp. 215–231.

    Article  MATH  MathSciNet  Google Scholar 

  32. A. Zygmund,Trigonometrical series, Warsaw (1935), p. 34.

  33. A. Zygmund,Trigonometrical series, vol. I, Cambridge (1959), p. 186.

    Google Scholar 

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Sharma, P.L., Kathal, P.D. A study of the matrix method of summability of the trigonometrical series. Rend. Circ. Mat. Palermo 19, 243–270 (1970). https://doi.org/10.1007/BF02845956

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