References
Cheng, Min-Teh: Summability factors of Fourier series. Duke Math. J.15, 17–27 (1948).
Chow, Hung Ching: On the summability factors of Fourier series. J. London Math. Soc.16, 215–220 (1941).
Fekete, M.: Zur Theorie der divergenten Reihen. Mathematikai és termeszettudomanyi értesitö (Budapest).29, 719–726 (1911).
—: On the absolute summability (A) of infinite series. Proc. Edinburgh Math. Soc. (2)3, 132–134 (1932).
Hardy, G. H., etJ. E. Littlewood: Sur la série de Fourier d'une fonction à carré sommable. Comptes Rendus Hebdomadaires des Séances de l'Académie des Sciences (Paris)156, 1307–1309 (1913).
—— The strong summability of Fourier series. Fundamenta Mathematicae25, 162–189 (1935).
Izumi, S. andT. Kawata: Notes on Fourier series. III: Absolute Summability. Proc. Imperial Academy (Tokyo)14, 32–35 (1938).
Kogbetliantz, Ervand: Sur les séries absolument sommables par la méthode des moyennes arithmétiques. Bulletin des Sciences Math. (2)49, 234–256 (1925).
Kogbetliant, Ervand Sommation des séries et intégrales divergentes par les moyennes arithmétiques et typiques. Mémorial des Sciences Mathématiques No. 51 (1931).
Marcinkiewicz, J.: Sur la sommabilite forte de séries de Fourier. J. London Math. Soc.14, 162–168 (1939).
Pati, T.: The summability factors of infinite series. Duke Math. J.21, 271–284 (1954).
— Absolute Cesàro summability factors of infinite series. Math. Z.78, 285–292 (1962).
Prasad, B. N.: On the summability of Fourier series and the bounded variation of power series. Proc. London Math. Soc. (2)35, 407–424 (1933).
—, andS. N. Bhatt: The summability factors of a Fourier series. Duke Math. J.24, 103–120 (1957).
Titchmarsh, E. C.: The Theory of Functions. Oxford 1949.
Whittaker, J. M.: The absolute summability of Fourier series. Proc. Edinburgh Math. Soc. (2)2, 1–5 (1930).
Zygmund, Antoni: Trigonometrical Series. Warsaw 1935.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pati, T. On an unsolved problem in the theory of absolute summability factors of Fourier series. Math Z 82, 106–114 (1963). https://doi.org/10.1007/BF01111799
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01111799