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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Convergence criteria for double Fourier series
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by J. J. Gergen PDF
Trans. Amer. Math. Soc. 35 (1933), 29-63 Request permission
References
    Adams, C. R., to be published. Carathéodory, C., Vorlesungen über Reelle Funktionen, Leipzig and Berlin, 1927.
  • Gaylord M. Merriman, On Certain Theorems Regarding Summable Series and Their Application to the Double and Triple Fourier’s Series, Amer. J. Math. 47 (1925), no. 2, 125–139. MR 1506550, DOI 10.2307/2370640
    • Gergen, J. J., Convergence and summability criteria for Fourier series, Quarterly Journal of Mathematics, Oxford Series, vol. 1 (1930), pp. 252-275. Hardy, G. H., On double Fourier series, Quarterly Journal of Pure and Applied Mathematics, vol. 37 (1905), pp. 53-79. —On certain convergence criteria for Fourier series, Messenger of Mathematics, vol. 49 (1919-20), pp. 149-155. Hardy, G. H. and Littlewood, J. E., Solution of the Cesáro summability problem for power series and Fourier series, Mathematische Zeitschrift, vol. 19 (1923), pp. 67-96. Hobson, E. W., Theory of Functions of a Real Variable, Cambridge, vol. 1, 1927. —Theory of Functions of a Real Variable, Cambridge, vol. 2, 1926. Küstermann, W. W., Über Fouriersche Doppelreihen, Inaugural Dissertation, München, 1913.
  • Henri Lebesgue, Sur l’intégration des fonctions discontinues, Ann. Sci. École Norm. Sup. (3) 27 (1910), 361–450 (French). MR 1509126
    • Pringsheim, A., Elementare Theorie der unendlichen Doppelreihen, Sitzungsberichte der Mathematisch-Physikalischen Classe der Akademie der Wissenschaften zu München, vol. 27 (1897), pp. 101-153. Tonelli, L., Serie Trigonometriche, Bologna, 1928.
  • Leonida Tonelli, Sulla convergenza delle serie doppie di Fourier, Ann. Mat. Pura Appl. 4 (1927), no. 1, 29–72 (Italian). MR 1553098, DOI 10.1007/BF02409984
    • Young, W. H., Multiple Fourier series, Proceedings of the London Mathematical Society, vol. 11 (1913), pp. 133-184. —On multiple integrals, Proceedings of the Royal Society of London, vol. 93 (1916-17), pp. 28-42.
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Additional Information
  • © Copyright 1933 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 35 (1933), 29-63
  • MSC: Primary 42B10
  • DOI: https://doi.org/10.1090/S0002-9947-1933-1501671-1
  • MathSciNet review: 1501671