Circular summation and localization of double trigonometric series
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- by Leonard D. Berkovitz
- Trans. Amer. Math. Soc. 70 (1951), 323-344
- DOI: https://doi.org/10.1090/S0002-9947-1951-0040464-2
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References
- Salomon Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. 40 (1936), no. 2, 175–207. MR 1501870, DOI 10.1090/S0002-9947-1936-1501870-1 G. H. Hardy, The second theorem of consistency for summable series, Proc. London Math. Soc. (2) vol. 15 (1916) pp. 72-88. G. H. Hardy and Marcel Riesz, The general theory of Dirichlet’s series, Cambridge, 1915.
- Charles N. Moore, On the summability of the double Fourier’s series of discontinuous functions, Math. Ann. 74 (1913), no. 4, 555–572. MR 1511782, DOI 10.1007/BF01456913
- K. Sokół-Sokołowski, On trigonometric series conjugate to Fourier series of two variables, Fund. Math. 34 (1947), 166–182. MR 21619, DOI 10.4064/fm-34-1-166-182
- A. Zygmund, Sur la théorie riemannienne des séries trigonométriques, Math. Z. 24 (1926), no. 1, 47–104 (French). MR 1544748, DOI 10.1007/BF01216767 —, Trigonometrical series, Warsaw, 1935.
Bibliographic Information
- © Copyright 1951 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 70 (1951), 323-344
- MSC: Primary 42.4X
- DOI: https://doi.org/10.1090/S0002-9947-1951-0040464-2
- MathSciNet review: 0040464