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Transactions of the American Mathematical Society

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Haar series


Author: James R. McLaughlin
Journal: Trans. Amer. Math. Soc. 137 (1969), 153-176
MSC: Primary 42.16
MathSciNet review: 0236605
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  • [1] G. Alexits, Convergence problems of orthogonal series, Translated from the German by I. Földer. International Series of Monographs in Pure and Applied Mathematics, Vol. 20, Pergamon Press, New York-Oxford-Paris, 1961. MR 0218827
  • [2] L. A. Balašov, On series with gaps, Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 631–644 (Russian). MR 0179504
  • [3] N. K. Bari, Trigonometricheskie ryady, With the editorial collaboration of P. L. Ul′janov, Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1961 (Russian). MR 0126115
  • [4] Z. Ciesielski and J. Musielak, On absolute convergence of Haar series, Colloq. Math. 7 (1959), 61–65. MR 0109980
  • [5] J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
  • [6] G. Faber, Über die Orthogonalfunktionen des Herrn Haar, Jber. Deutsch. Math.-Verein. 19 (1910), 104-112.
  • [7] B. I. Golubov, Fourier series of continuous functions relative to a Haar system, Dokl. Akad. Nauk SSSR 156 (1964), 247–250 (Russian). MR 0162093
  • [8] B. I. Golubov, On Fourier series of continuous functions with respect to a Haar system, Izv. Akad. Nauk SSSR Ser. Mat. 28 (1964), 1271–1296 (Russian). MR 0172057
  • [9] F. R. Keogh, On Rademacher series with bounded sum, J. London Math. Soc. 33 (1958), 454–455. MR 0101984
  • [10] V. A. Matveev, On Fourier-Haar coefficients, Izv. Vysš. Učebn. Zaved. Matematika 1965 (1965), no. 6 (49), 103–112 (Russian). MR 0190620
  • [11] V. A. Matveev, Variation of a function and the Fourier coefficients with respect to the Haar and Schauder systems, Izv. Akad. Nauk SSSR Ser. Mat. 30 (1966), 1397–1419 (Russian). MR 0204969
  • [12] James R. McLaughlin, Functions represented by Rademacher series, Pacific J. Math. 27 (1968), 373–378. MR 0238021
  • [13] M. E. Munroe, Introduction to measure and integration, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1953. MR 0053186
  • [14] A. M. Olevskiĭ, Divergent Fourier series of continuous functions, Dokl. Akad. Nauk SSSR 141 (1961), 28–31 (Russian). MR 0132959
  • [15] A. M. Olevskiĭ, The divergence of orthogonal series and the Fourier coefficients of continuous functions with respect to complete systems, Sibirsk. Mat. Ž. 4 (1963), 647–656 (Russian). MR 0155141
  • [16] W. Orlicz, Theorie der Orthogonalwicklungen. III, Bull. Acad. Polon. Sci. Sér. Sci. A. 1932, 229-238.
  • [17] A. I. Rubinšteĭn, On gap series, Izv. Vysš. Učebn. Zaved. Matematika 1963 (1963), no. 3 (34), 137–148 (Russian). MR 0152809
  • [18] Wang Si-lei, On Haar series, Chinese Math.–Acta 8 (1966), 222–233. MR 0201914
  • [19] Otto Szász, Quasi-monotone series, Amer. J. Math. 70 (1948), 203–206. MR 0022917
  • [20] V. A. Skvorcov, A theorem of Cantor type for the Haar system, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1964 (1964), no. 5, 3–6 (Russian, with English summary). MR 0170161
  • [21] P. L. Ul′janov, Divergent Fourier series, Uspehi Mat. Nauk 16 (1961), no. 3 (99), 61–142 (Russian). MR 0125398
  • [22] -, Haar series, Dokl. Akad. Nauk SSSR 148 (1963), 532-534=Soviet Math. Dokl. 4 (1963), 437-440.
  • [23] P. L. Ul′janov, On Haar series, Mat. Sb. (N.S.) 63 (105) (1964), 356–391 (Russian). MR 0161086
  • [24] P. L. Ul′janov, Solved and unsolved problems in the theory of trigonometric and orthogonal series, Uspehi Mat. Nauk 19 (1964), no. 1 (115), 3–69 (Russian). MR 0161085
  • [25] P. L. Ul′janov, Haar series, Vestnik Moskov. Univ. Ser. I Mat. Meh. 1965 (1965), no. 4, 35–43 (Russian, with English summary). MR 0190621
  • [26] P. L. Ul′janov, Absolute and unconditional convergence, Dokl. Akad. Nauk SSSR 169 (1966), 536–538 (Russian). MR 0196387
  • [27] P. L. Ul′janov, Some properties of series with respect to the Haar system, Mat. Zametki 1 (1967), 17–24 (Russian). MR 0208260
  • [28] P. L. Ul′janov, Absolute and uniform convergence of Fourier series, Mat. Sb. (N.S.) 72 (114) (1967), 193–225 (Russian). MR 0206613
  • [29] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776

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DOI: https://doi.org/10.1090/S0002-9947-1969-0236605-8
Article copyright: © Copyright 1969 American Mathematical Society