On the Walsh functions
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- by N. J. Fine PDF
- Trans. Amer. Math. Soc. 65 (1949), 372-414 Request permission
References
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M. Kac, Sur les fonctions ${2^n}t - [{2^n}t] - 1/2$, J. London Math. Soc. vol. 13 (1938) pp. 131-134.
- M. Kac, On the distribution of values of sums of the type $\sum f(2^k t)$, Ann. of Math. (2) 47 (1946), 33–49. MR 15548, DOI 10.2307/1969033 S. Kaczmarz, Über ein Orthogonalsystem, Comptes Rendus du premier congrès des mathématiciens des pays slaves, Warsaw, 1929, pp. 189-192. S. Kaczmarz and H. Steinhaus, Le systeme orthogonal de M. Rademacher, Studia Math. vol. 2 (1930) pp. 231-247. R. E. A. C. Paley, A remarkable series of orthogonal functions, Proc. London Math. Soc. vol. 34 (1932) pp. 241-279.
- 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
- J. L. Walsh, A Closed Set of Normal Orthogonal Functions, Amer. J. Math. 45 (1923), no. 1, 5–24. MR 1506485, DOI 10.2307/2387224 A. Zygmund, Trigonometrical series, Warsaw, 1935.
Additional Information
- © Copyright 1949 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 65 (1949), 372-414
- MSC: Primary 42.4X
- DOI: https://doi.org/10.1090/S0002-9947-1949-0032833-2
- MathSciNet review: 0032833