Queffélec, Martine Mesures spectrales associées à certaines suites arithmétiques. (French) Zbl 0435.42007 Bull. Soc. Math. Fr. 107, 385-421 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 13 Documents MSC: 11K70 Harmonic analysis and almost periodicity in probabilistic number theory 42A55 Lacunary series of trigonometric and other functions; Riesz products Keywords:spectral measure; arithmetical sequences; Gel’fand transform; generalized characters × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML References: [1] BÉSINEAU (J.) . - Indépendance stochastique d’ensembles liés à la fonction ”somme des chiffres” , Acta Arithm., Warszawa, t. 20, 1972 , p. 401-416. Article | MR 46 #3470 | Zbl 0252.10052 · Zbl 0252.10052 [2] BROWN (G.) . - Riesz products and generalized characters , Proc. London math. Soc., Séries 3, t. 30, 1975 , p. 209-238. MR 51 #8737 | Zbl 0325.43003 · Zbl 0325.43003 · doi:10.1112/plms/s3-30.2.209 [3] BROWN (G.) . - Singular infinitely divisible distributions whose characteristic functions vanish at infinity , Proc. Camb. phil. Soc. (à paraître). Zbl 0366.60021 · Zbl 0366.60021 · doi:10.1017/S0305004100053913 [4] BROWN (G.) and MORAN (W.) . - A dichotomy for infinite convolutions of discrete measures , Proc. Camb. phil. Soc., t. 73, 1973 , p. 307-316. MR 47 #715 | Zbl 0247.43002 · Zbl 0247.43002 [5] BROWN (G.) and MORAN (W.) . - Bernoulli measure algebras , Acta Math., Uppsala, t. 132, 1974 , p. 77-109. MR 54 #5743 | Zbl 0278.43004 · Zbl 0278.43004 · doi:10.1007/BF02392109 [6] COQUET (J.) , KAMAE (T.) et MENDÈS FRANCE (M.) . - Sur la mesure spectrale de certaines suites arithmétiques , Bull. Soc. math. France, t. 105, 1977 , p. 369-384. Numdam | MR 57 #12439 | Zbl 0383.10035 · Zbl 0383.10035 [7] ELLISON (W. J.) et MENDÈS FRANCE (M.) . - Les nombres premiers . - Paris, Hermann, 1975 (Act. scient. et ind., 1366 ; Publ. Inst. Math. Univ. Nancago, 9). MR 54 #5138 | Zbl 0313.10001 · Zbl 0313.10001 [8] HOFFMAN (K.) . - Banach spaces of analytic functions . - Englewood Cliffs, Prentice Hall, 1962 (Prentice Hall Series in modern Analysis). MR 24 #A2844 | Zbl 0117.34001 · Zbl 0117.34001 [9] HOST (B.) et PARREAU (F.) . - Séminaire d’analyse harmonique , Villetaneuse, 1977 - 1978 (à paraître). [10] KAMAE (T.) . - Sum of digits to different bases and mutual singularity of their spectral measures , Osaka J. Math., t. 15, 1978 , p. 569-574. MR 80b:10073 | Zbl 0391.10034 · Zbl 0391.10034 [11] KAMAE (T.) . - Mutual singularity of spectra of dynamical systems given by ”sums of digits” to different bases , ”Systèmes dynamiques, I” [ 1977 , Warszawa], Astérisque, 1977 , p. 109-114. MR 58 #5566 | Zbl 0371.28018 · Zbl 0371.28018 [12] KEANE (M.) . - Stongly mixing g-measures , Invent. Math., t. 16, 1972 , p. 309-324. MR 46 #9295 | Zbl 0241.28014 · Zbl 0241.28014 · doi:10.1007/BF01425715 [13] MENDÈS FRANCE (M.) . - Nombres normaux. Applications aux fonctions pseudo-aléatoires , J. Anal. math., Jérusalem, t. 20, 1967 , p. 1-56 (Thèse Sc. math., Paris, 1966 ). MR 36 #3735 | Zbl 0161.05002 · Zbl 0161.05002 · doi:10.1007/BF02786669 [14] PEYRIÈRE (J.) . - Sur les produits de Riesz , C. R. Acad. Sc. Paris, t. 276, 1973 , p. 1417-1419. MR 47 #5512 | Zbl 0258.43002 · Zbl 0258.43002 [15] PEYRIÈRE (J.) . - Étude de quelques propriétés des produits de Riesz , Ann. Inst. Fourier, Grenoble, t. 25, 1975 , n^\circ 2, p. 127-169. Numdam | MR 53 #8771 | Zbl 0302.43003 · Zbl 0302.43003 · doi:10.5802/aif.557 [16] QUEFFELEC (Martine) . - Sur la singularité des produits de Riesz et des mesures spectrales associées à la somme des chiffres (à paraître). · Zbl 0429.10035 · doi:10.1007/BF02760612 [17] RUDIN (W.) . - Fourier analysis on groups . - New York, Interscience publ., 1962 (Interscience Tracts in pure and appl. Mathematics, 12). MR 27 #2808 | Zbl 0107.09603 · Zbl 0107.09603 [18] ŠREJDER (A.) . - The structure of maximal ideals in rings of measures with convolutions , Mat. Sbornik [en russe], N. S., t. 27, (69), 1950 , p. 297-318. MR 12,420c | Zbl 0038.27302 · Zbl 0038.27302 [19] TAYLOR (J. D.) . - Measure algebras . - Providence, American mathematical Society, 1973 (Conference Board of the mathematical Sciences. Regional Conference Series in Mathematics, 16). Zbl 0269.28001 · Zbl 0269.28001 [20] WIENER (N.) . - The Fourier integral and certain of its applications . - Cambridge, University Press, 1933 [réédition Dover Publications, 1958 ]. Zbl 0006.05401 | JFM 59.0416.01 · Zbl 0006.05401 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.