Salem, R. Sets of uniqueness and sets of multiplicity. I, II. (English) Zbl 0060.18604 Trans. Am. Math. Soc. 54, 218-228 (1943); 56, 32-49 (1944). Reviewer: L. Cesari Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 17 Documents 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 × Cite Format Result Cite Review PDF Full Text: DOI DOI References: [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 [5] Paul Erdös, On a family of symmetric Bernoulli convolutions, Amer. J. Math. 61 (1939), 974 – 976. · JFM 65.1308.01 · doi:10.2307/2371641 [6] P. Fatou, Séries trigonométriques et séries de Taylor, Acta Math. 30 (1906), no. 1, 335 – 400 (French). · JFM 37.0283.01 · doi:10.1007/BF02418579 [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.