Tohoku Mathematical Journal

Notes on Fourier analysis (XVIII): Absolute summability of series with constant terms

Gen-ichirô Sunouchi

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 1, Number 1 (1949), 57-65.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178245769

Digital Object Identifier
doi:10.2748/tmj/1178245769

Mathematical Reviews number (MathSciNet)
MR0034861

Zentralblatt MATH identifier
0041.39101

Subjects
Primary: 40.0X

Citation

Sunouchi, Gen-ichirô. Notes on Fourier analysis (XVIII): Absolute summability of series with constant terms. Tohoku Math. J. (2) 1 (1949), no. 1, 57--65. doi:10.2748/tmj/1178245769. https://projecteuclid.org/euclid.tmj/1178245769


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References

  • [1] Bosanquet, L. S., An analogue of Mercer's theorem, Journ. London Math. Soc. 13 (1931), 177-180.
  • [2] Bosanquet, L. S., and Kestelman, I.I., The absolute convergence of series of integrals, Pnc, London Math. Soc. 45 (1938), 88-97.
  • [3] Gelfand, I., Abstrakte Funktionen und linearie Operatoten, Rcueil Math. (1938), 235-284
  • [4] Hayashi, G., A theorem on limit, Thok Math. Journ. 45 (1939), 29-31.
  • [5] Izumi, S., Uber die lineare Transformation in der Theorie der unerdliche Beihen, T(A)hoku Math. Journ., 27, 313-323.
  • [6] Sunouchi, G., On Mercer's theorem, Proc. Imp. Acad. Tokyo, (under the press)
  • [7] Hyslop, J. M., A Tauberian theorem for absolute suminability, Journ Londo Math. Soc. 2, 176-180.

See also

  • Part VIII: Shin-ichi Izumi. Notes on Fourier analysis (VIII): Local properties of Fourier series. Tohoku Math. J., Volume 1, Number 2 (1950), pp. 136-143.
  • Part XIV: Noboru Matsuyama. Notes on Fourier analysis (XIV): Absolute Cesàro summability of Fourier series. Tohoku Math. J., Volume 1, Number 1 (1949), pp. 40-45.
  • Part XV: Shigeki Yano. Notes on Fourier analysis (XV): On the absolute convergence of trigonometrical series. Tohoku Math. J., Volume 1, Number 1 (1949), pp. 46-49.
  • Part XVI: Shin-ichi Izumi. Notes on Fourier analysis (XVI). Tohoku Math. J., Volume 1, Number 2 (1950), pp. 144-166.
  • Part XVI: Shin-ichi Izumi. Notes on Fourier analysis (XVI): On the strong law of large numbers and gap series. Tohoku Math. J., Volume 3, Number 1 (1951), pp. 89-103.
  • Part XVII: Sigeki Yano. Notes on Fourier analysis (XVII): The integrated Lipschitz condition of a function and Fejér mean of Fourier series. Tohoku Math. J., Volume 1, Number 1 (1949), pp. 50-56.
  • Part XIX: Shigeki Yano. Notes on Fourier analysis (XIX): A remark on Riemann sums. Tohoku Math. J., Volume 2, Number 1 (1950), pp. 1-3.
  • Part XX: Noboru Matsuyama. Notes on Fourier analysis (XX): On the Riesz logarithmic summability of the derived Fourier series. Tohoku Math. J., Volume 1, Number 1 (1949), pp. 91-94.
  • Part XXV: Genichirô Sunouchi. Notes on Fourier analysis (XXV): Quasi-Tauberian theorem. Tohoku Math. J., Volume 1, Number 2 (1950), pp. 167-185.
  • Part XXV: Noboru Matsuyama. Notes on Fourier analysis (XXV): On the $\vert C\vert $-summability of the Fourier Series. Tohoku Math. J., Volume 2, Number 1 (1950), pp. 51-56.
  • Part XXVI: Tamotsu Tsuchikura. Notes on Fourier analysis (XXVI): Lipschitz condition of partial sums of Fourier series. Tohoku Math. J., Volume 2, Number 1 (1950), pp. 24-29.
  • Part XXVI: Shin-ichi Izumi. Note on Fourier analysis (XXVI): Some negative examples in the theory of Fourier series. Tohoku Math. J., Volume 2, Number 1 (1950), pp. 74-95.
  • Part XXVII: Shin-ichi Izumi. Notes on Fourier analysis (XXVII): A theorem on Cesàro summation. Tohoku Math. J., Volume 3, Number 2 (1951), pp. 212-215.
  • Part XXXV: Shin-ichi Izumi. Note on Fourier analysis (XXXV). Tohoku Math. J., Volume 1, Number 3 (1950), pp. 285-302.
  • Part XXXVI: Gen-ichiro Sunouchi. Notes on Fourier analysis (XXXVI): On certain applications of Wiener's Tauberian theorems. Tohoku Math. J., Volume 1, Number 3 (1950), pp. 303-312.
  • Part XXXVII: Noboru Matsuyama. Notes on Fourier analysis (XXXVII): On the convergence factor of the Fourier series at a point. Tohoku Math. J., Volume 2, Number 2 (1950), pp. 126-134.
  • Part XXXIX: Shin-ichi Izumi, Gen-ichirô Sunouchi. Notes on Fourier analysis (XXXIX):Theorems concerning Cesàro summability. Tohoku Math. J., Volume 1, Number 3 (1950), pp. 313-326.
  • Part XXXIX: Gen-ichirô Sunouchi. Notes on Fourier analysis (XXXIX). Tohoku Math. J., Volume 3, Number 1 (1951), pp. 71-88.
  • Part XL: Noboru Matsuyama. Notes on Fourier analysis (XL): On the absolute summability of the Fourier series. Tohoku Math. J., Volume 3, Number 1 (1951), pp. 39-44.
  • Part XLIV: Gen-ichirô Sunouchi. Notes on Fourier analysis (XLIV): On the summation of Fourier series. Tohoku Math. J., Volume 3, Number 1 (1951), pp. 114-122.
  • Part XLVI: Gen-ichirô Sunouchi. Notes on Fourier analysis (XLVI): A convergence criterion for Fourier series. Tohoku Math. J., Volume 3, Number 2 (1951), pp. 216-219.
  • Part XLVIII: Shin-ichi Izumi, Gen-ichirô Sunouchi. Notes on Fourier analysis (XLVIII): Uniform convergence of Fourier series. Tohoku Math. J., Volume 3, Number 3 (1951), pp. 298-305.
  • Part XLIX: S. Izumi, N. Matsuyama, T. Tsuchikura. Notes on Fourier analysis (XLIX): Some negative examples. Tohoku Math. J., Volume 5, Number 1 (1953), pp. 43-51.