On the summability of Fourier series. I

Authors:
Einar Hille and J. D. Tamarkin

Journal:
Trans. Amer. Math. Soc. **34** (1932), 757-783

MSC:
Primary 42A24

DOI:
https://doi.org/10.1090/S0002-9947-1932-1501662-X

MathSciNet review:
1501662

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**[1]**Griffith C. Evans,*Complements of Potential Theory*, Amer. J. Math.**54**(1932), no. 2, 213–234. MR**1506886**, https://doi.org/10.2307/2370985**[2]**G. H. Hardy,*Theorems relating to the summability and convergence of slowly oscillating series*, Proceedings of the London Mathematical Society, (2), vol. 8 (1910), pp. 301-320.**[3]**G. H. Hardy,*The summability of a Fourier series by logarithmic means*, Quarterly Journal of Mathematics (Oxford series), vol. 2 (1931), pp. 107-112.**[4]**E. Hille and J. D. Tamarkin,*On the summability of Fourier series*, Proceedings of the National Academy of Sciences, vol. 14 (1928), pp. 915-918.**[5]**David Sherman Morse,*Relative Inclusiveness of Certain Definitions of Summability*, Amer. J. Math.**45**(1923), no. 4, 259–285. MR**1506508**, https://doi.org/10.2307/2370574**[6]**N. E. Nörlund,*Sur une application des fonctions permutables*, Lunds Universitets Årsskrift, (N.F.), avd. 2, 16, No. 3 (1920); 10 pp.**[7]**M. Riesz,*Sur l'équivalence de certaines méthodes de sommation*, Proceedings of the London Mathematical Society, (2), vol. 22 (1924), pp. 412-419.**[8]**G. F. Woronoi,*Extension of the notion of the limit of the sum of terms of an infinite series*, Ann. of Math. (2)**33**(1932), no. 3, 422–428. MR**1503066**, https://doi.org/10.2307/1968525

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DOI:
https://doi.org/10.1090/S0002-9947-1932-1501662-X

Article copyright:
© Copyright 1932
American Mathematical Society