On Walsh-Fourier series

Morgenthaler, George W.

doi:10.1090/S0002-9947-1957-0091370-4

On Walsh-Fourier series
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by George W. Morgenthaler

Trans. Amer. Math. Soc. 84 (1957), 472-507

DOI: https://doi.org/10.1090/S0002-9947-1957-0091370-4

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References

N. J. Fine, On the Walsh functions, Trans. Amer. Math. Soc. 65 (1949), 372–414. MR 32833, DOI 10.1090/S0002-9947-1949-0032833-2
N. J. Fine, The generalized Walsh functions, Trans. Amer. Math. Soc. 69 (1950), 66–77. MR 42535, DOI 10.1090/S0002-9947-1950-0042535-2
N. J. Fine, Cesàro summability of Walsh-Fourier series, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 588–591. MR 70757, DOI 10.1073/pnas.41.8.588
Paul R. Halmos, Measure Theory, D. Van Nostrand Co., Inc., New York, N. Y., 1950. MR 0033869
T. H. Hildebrandt, Definitions of Stieltjes Integrals of the Riemann Type, Amer. Math. Monthly 45 (1938), no. 5, 265–278. MR 1524276, DOI 10.2307/2302540
E. Hille and J. D. Tamarkin, Remarks on a Known Example of a Monotone Continuous Function, Amer. Math. Monthly 36 (1929), no. 5, 255–264. MR 1521732, DOI 10.2307/2298506

On the differentiability of functions and summability of trigonometrical series

Beiträge zur Theorie der Orthogonalentwicklungen

A remarkable series of orthogonal functions

Hans Rademacher, Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen, Math. Ann. 87 (1922), no. 1-2, 112–138 (German). MR 1512104, DOI 10.1007/BF01458040
R. Salem and A. Zygmund, On a theorem of Banach, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 293–295. MR 21611, DOI 10.1073/pnas.33.10.293
R. Salem and A. Zygmund, On lacunary trigonometric series, Proc. Nat. Acad. Sci. U.S.A. 33 (1947), 333–338. MR 22263, DOI 10.1073/pnas.33.11.333
A. A. Šneĭder, On series of Walsh functions with monotonic coefficients, Izv. Akad. Nauk SSSR Ser. Mat. 12 (1948), 179–192 (Russian). MR 0025605
A. A. Šneĭder, On the uniqueness of expansions in Walsh functions, Mat. Sbornik N.S. 24(66) (1949), 279–300 (Russian). MR 0032834
A. A. Šneĭder, On the convergence of subsequences of the partial sums of Fourier series of Walsh functions, Doklady Akad. Nauk SSSR (N.S.) 70 (1950), 969–971 (Russian). MR 0032835
Gen-Ichirô Sunouchi, On the Walsh-Kaczmarz series, Proc. Amer. Math. Soc. 2 (1951), 5–11. MR 41259, DOI 10.1090/S0002-9939-1951-0041259-1
N. Vilenkin, On a class of complete orthonormal systems, Bull. Acad. Sci. URSS. Sér. Math. [Izvestia Akad. Nauk SSSR] 11 (1947), 363–400 (Russian, with English summary). MR 0022560
Shigeki Yano, On Walsh-Fourier series, Tohoku Math. J. (2) 3 (1951), 223–242. MR 45236, DOI 10.2748/tmj/1178245527
Shigeki Yano, On approximation by Walsh functions, Proc. Amer. Math. Soc. 2 (1951), 962–967. MR 45235, DOI 10.1090/S0002-9939-1951-0045235-4

Quelques théorèmes sur les séries trigonométriques et celles de puissances

Trigonometrical series