Nazarov, F. L. On the theorems of Turán, Amrein-Berthier, and Zygmund. (English. Russian original) Zbl 0842.42001 J. Math. Sci., New York 78, No. 2, 195-198 (1996); translation from Zap. Nauchn. Semin. POMI 201, 117-123 (1992). Summary: A rather sharp inequality of Turán’s lemma type is obtained. Its applications to some uniqueness theorems are discussed. No proofs are given.[This note is an annotation of the author’s paper published in Algebra Anal. 5, No. 4, 3–66 (1993; Zbl 0801.42001); English translation in St. Petersbg. Math. J. 5, No. 4, 663–717 (1994)]. Cited in 1 ReviewCited in 1 Document MSC: 42A05 Trigonometric polynomials, inequalities, extremal problems 42A55 Lacunary series of trigonometric and other functions; Riesz products 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type Keywords:Turan type lemma; exponential polynomial; uncertainty principle in harmonic analysis; lacunary trigonometric series; Morgan’s theorem; Fourier transforms Citations:Zbl 0822.42001; Zbl 0355.42015; Zbl 0009.24801; Zbl 0801.42001 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] I. M. Mikheev, ”On lacunary series,”Mat. Sb. (N. S.),98, (140), No. 4 (12), 538–563 (1975). [2] A. Zigmund,Trigonometric Series, 2nd ed., Vols. I, II, Cambridge Univ. Press, New York (1959). [3] P. P. Kargaev, ”Nonlocal almost differential operators and interpolation by functions with a sparse spectrum,”Mat. Sb. (N.S.),128(170), No. 1, 133–142 (1985). [4] S. Mandelbrojt,Quasianalytic classes of functions [in Russian], GITTL, Moscow-Leningrad (1937). [5] W. O. Amrein, A. M. Berthier, ”On support properties ofL p -functions and their Fourier transforms,”J. Funct. Anal.,24, No. 3, 258–267 (1977). · Zbl 0355.42015 · doi:10.1016/0022-1236(77)90056-8 [6] J. W. Morgan, ”A note on Fourier transform,”J. London Math. Soc.,9, No. 3, 187–192 (1934). · Zbl 0009.24801 · doi:10.1112/jlms/s1-9.3.187 [7] P. Turan,Eine neue Methode in der Analyses und deres Anwendungen, Akádémiai Kiadó, Budapest (1953). [8] D. Gaier, ”Bemerkungen zum Turanschen Lemma,”Abhandlungen Math. Semin. Univ. Hamburg,135, Nos. 1–2, 1–7 (1970). · Zbl 0205.37803 · doi:10.1007/BF02992468 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.