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Transactions of the American Mathematical Society

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Orthonormal sets of periodic functions of the type $ \{f(nx)\}$

Authors: D. G. Bourgin and C. W. Mendel
Journal: Trans. Amer. Math. Soc. 57 (1945), 332-363
MSC: Primary 42.4X
MathSciNet review: 0012158
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  • [1] S. Banach, Théorie des opérations linéaires, Warsaw, 1932.
  • [2] M. H. Stone, Linear transformations in Hilbert space, Amer. Math. Soc. Colloquium Publications, vol. 15, 1932. MR 1451877 (99k:47001)
  • [3] E. Hopf, Ergoden Theorie, Ergebnisse der Mathematik, 1937.
  • [4] E. C. Titchmarsh, The theory of functions, 2nd ed., Oxford University Press, 1939. MR 0197687 (33:5850)
  • [5] D. V. Widder, The Laplace transform, Princeton University Press, 1941. MR 0005923 (3:232d)
  • [6] A. Zygmund, Trigonometrical series, Warsaw, 1933.
  • [7] E. E. Kummer, Beitrag zur Theorie der Funktion $ \Gamma (x)$, Zeitschrift für reine und angewandte Mathematik vol. 35 (1847) pp. 1-4.
  • [8] G. H. Hardy and J. E. Littlewood, On the absolute convergence of Fourier series, J. London Math. Soc. vol. 3 (1928) pp. 250-253.
  • [9] M. H. Stone, A characteristic property of certain sets of trigonometrical functions, Amer. J. Math. vol. 49 (1927) pp. 535-542. MR 1506643
  • [10] E. Landau, Über den Wertevorrat von $ \zeta (s)$ in der Halbebene $ \sigma > 1$, Nachr. Ges. Wiss. Göttingen (1933) pp. 81-91.

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