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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Integrals and summable trigonometric series
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by R. D. James PDF
Bull. Amer. Math. Soc. 61 (1955), 1-15
References
    1. J. C. Burkill, The expression of trigonometrical series in Fourier form, J. London Math. Soc. vol. 11 (1936) pp. 43-48.
  • J. C. Burkill, Integrals and trigonometric series, Proc. London Math. Soc. (3) 1 (1951), 46–57. MR 42533, DOI 10.1112/plms/s3-1.1.46
    • 3. A. Denjoy, La totalisation des nombres dérivés non sommables, Ann. École Norm. (3) vol. 33 (1916) pp. 127-222; vol. 34 (1917) pp. 181-236. 4. A. Denjoy, Calcul des coefficients d’une série trigonométrique partout convergente, C. R. Acad. Sci. Paris vol. 172 (1921) pp. 653-655, 833-835, 903-906, 1218-1221; vol. 173 (1921) pp. 127-129. 5. A. Denjoy, Leçons sur le calcul des coefficients d’une série trigonométrique, Paris, 1941 and 1949.
  • G. H. Hardy, Divergent Series, Oxford, at the Clarendon Press, 1949. MR 0030620
  • R. D. James and Walter H. Gage, A generalized integral, Trans. Roy. Soc. Canada Sect. III 40 (1946), 25–35. MR 21081
  • R. D. James, A generalized integral. II, Canad. J. Math. 2 (1950), 297–306. MR 36344, DOI 10.4153/cjm-1950-027-4
  • R. D. James, Generalized $n$th primitives, Trans. Amer. Math. Soc. 76 (1954), 149–176. MR 60002, DOI 10.1090/S0002-9947-1954-0060002-0
    • 10. J. Marcinkiewicz and A. Zygmund, On the differentiability of functions and summability of trigonometrical series, Fund. Math. vol. 26 (1936) pp. 1-43.
  • Ludwig Neder, Zur Theorie der trigonometrischen Reihen, Math. Ann. 84 (1921), no. 1-2, 117–136 (German). MR 1512024, DOI 10.1007/BF01458697
    • 12. M. Riesz, Über summierbare trigonometrische Reihen, Math. Ann. vol. 71 (1912) pp. 54-75. 13. S. Saks, Theory of the integral, Warsaw, 1937. 14. S. Verblunsky, On the theory of trigonometric seriesVII, Fund. Math. vol. 23 (1934) pp. 193-235.
  • František Wolf, On summable trigonometrical series: an extension of uniqueness theorems, Proc. London Math. Soc. 45 (1939), 328–356. MR 0001369, DOI 10.1112/plms/s2-45.1.328
    • 16. A. Zygmund, Sur la théorie riemannienne des séries trigonométriques, Math. Zeit. vol. 24 (1926) pp. 47-104. 17. A. Zygmund, Trigonometrical series, Warsaw, 1935.
Additional Information
  • Journal: Bull. Amer. Math. Soc. 61 (1955), 1-15
  • DOI: https://doi.org/10.1090/S0002-9904-1955-09853-7
  • MathSciNet review: 0067228