Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Arithmetric structure and lacunary Fourier series

Author: George Benke
Journal: Proc. Amer. Math. Soc. 34 (1972), 128-132
MSC: Primary 43A45
MathSciNet review: 0301456
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a theorem concerning the arithmetic structure of $ \Lambda (p)$ sets. This generalizes a result of Rudin and yields a new characterization of Sidon sets for certain Abelian groups.

References [Enhancements On Off] (What's this?)

  • [1] A. Horn, A characterization of unions of linearly independent sets, J. London Math. Soc. 30 (1955), 494-496. MR 17, 135. MR 0071487 (17:135d)
  • [2] J. P. Kahane, Some random series of functions, Heath, Lexington, Mass., 1968. MR 40 #8095. MR 0254888 (40:8095)
  • [3] M. P. Malliavin-Brameret and P. Malliavin, Caractérisation arithmétique d'une classe d'ensembles de Helson, C. R. Acad. Sci. Paris 264 (1967), 192-193.
  • [4] W. Rudin, Fourier analysis on groups, Interscience Tracts in Pure and Appl. Math., no. 12, Interscience, New York, 1962. MR 27 #2808. MR 0152834 (27:2808)
  • [5] -, Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203-227. MR 22 #6972. MR 0116177 (22:6972)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 43A45

Retrieve articles in all journals with MSC: 43A45

Additional Information

Keywords: Lacunary Fourier series, Sidon sets, $ \Lambda (p)$ sets
Article copyright: © Copyright 1972 American Mathematical Society

American Mathematical Society