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Sets of uniqueness and sets of multiplicity. I, II. (English) Zbl 0060.18604


MSC:

42A63 Uniqueness of trigonometric expansions, uniqueness of Fourier expansions, Riemann theory, localization
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
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[1] Bary, Nina Sur l’unicité du développement trigonométrique, Fund. Math. vol. 9 (1927) pp. 62-118. · JFM 53.0261.01
[2] -Sur la nature diophantique du problème d’unicité du développement trigonométrique, C. R. Acad. Sci. Paris vol. 202 (1936) p. 1901.
[3] -Sur le rôle des lois diophantiques dans le problème d’unicité du développement trigonométrique, Rec. Math. (Mat. Sbornik) N.S. vol. 2 (1937) pp. 699-722. · Zbl 0018.01801
[4] Carleman, T. Sur les équations intégrales singulières a noyau réel et symétrique, Uppsala University Årsskrift, 1923. · JFM 49.0272.01
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[7] Børge Jessen and Aurel Wintner, Distribution functions and the Riemann zeta function, Trans. Amer. Math. Soc. 38 (1935), no. 1, 48 – 88. · Zbl 0014.15401
[8] Richard Kershner, On Singular Fourier-Stieltjes Transforms, Amer. J. Math. 58 (1936), no. 2, 450 – 452. · Zbl 0013.30002 · doi:10.2307/2371053
[9] Marcinkiewicz, J. and Zygmund, A. Two theorems on trigonometrical series, Rec. Math. (Mat. Sbornik) N. S. vol. 2 (1937) pp. 733-737. · Zbl 0018.01802
[10] Charles Pisot, La répartition modulo 1 et les nombres algébriques, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (2) 7 (1938), no. 3-4, 205 – 248 (French). · Zbl 0019.15502
[11] Pólya, G. and Szegö, G. Aufgaben und Lehrsätze aus der Analysis, Berlin, 1925. · JFM 51.0173.01
[12] Alexandre Rajchman, Sur la multiplication des séries trigonométriques et sur une classe remarquable d’ensembles fermés, Math. Ann. 95 (1926), no. 1, 389 – 408 (French). · JFM 51.0220.01 · doi:10.1007/BF01206617
[13] Alexandre Rajchman, Une classe de séries trigonométriques qui convergent presque partout vers zéro, Math. Ann. 101 (1929), no. 1, 686 – 700 (French). · JFM 55.0162.04 · doi:10.1007/BF01454869
[14] Raphaël Salem, The absolute convergence of trigonometrical series, Duke Math. J. 8 (1941), 317 – 334. · Zbl 0025.31602
[15] R. Salem, On singular monotonic functions of the Cantor type, J. Math. Phys. Mass. Inst. Tech. 21 (1942), 69 – 82. · Zbl 0060.18606 · doi:10.1002/sapm194221169
[16] T. Vijayaraghavan, On the fractional parts of the powers of a number. II, Proc. Cambridge Philos. Soc. 37 (1941), 349 – 357. · JFM 67.0988.02
[17] Zygmund, A. Trigonometrical series, Warszawa-Lwow, 1935. · Zbl 0011.01703
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