ArticleOriginal scientific text

Title

Lacunary series on compact groups

Authors 1, 1

Affiliations

  1. Department of Mathematics, University of Missouri-Rolla, Rolla, MO 65409-0020, U.S.A.

Abstract

A theorem of Sidon concerning absolutely convergent Fourier series is extended to compact groups.

Bibliography

  1. Adams, K., Weighted Sidon sets, Ph.D. dissertation, Univ. of Missouri at Rolla, 1998.
  2. Cecchini, C., Lacunary Fourier series on compact Lie groups, J. Funct. Anal. 11 (1972), 191-203.
  3. Banach, S., Über einige Eigenschaften der lakunären trigonometrischen Reihen, Studia Math. 2 (1930), 207-220.
  4. Figà-Talamanca, A. and D. Rider, A theorem of Littlewood and lacunary series for compact groups, Pacific J. Math. 16 (1966), 505-514.
  5. Hare, K. and D. Wilson, Weighted p-Sidon sets, J. Austral. Math. Soc. 61 (1996), 73-95.
  6. Hewitt, E. and K. A. Ross, Abstract Harmonic Analysis, Vols. I and II, 2nd ed., Springer, New York, 1979.
  7. Hewitt, E. and H. S. Zuckerman, Some theorems on lacunary series with extensions to compact groups, Trans. Amer. Math. Soc. 93 (1959), 1-19.
  8. Hutchinson, M.F., Non-tall compact groups admit infinite Sidon sets, J. Austral. Math. Soc. 23 (1977), 467-475.
  9. López, J.H. and K. A. Ross, Sidon Sets, Marcel Dekker, New York, 1975.
  10. Marcus, M.B. and G. Pisier, Random Fourier Series with Applications to Harmonic Analysis, Princeton Univ. Press, Princeton, 1981.
  11. Pisier, G., Conditions d'entropie et caractérisations arithmétiques des ensembles de Sidon, in: Topics in Modern Harmonic Analysis, vol. II, Ist. Naz. Alta Mat. F. Severi, Roma, 1983, 911-944.
  12. Rider, D., Gap series on groups and spheres, Canad. J. Math. 18 (1966), 389-398.
  13. Rider, D., Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), 759-764.
  14. Rudin, W., Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203-208.
  15. Rudin, W., Fourier Analysis on Groups, Wiley, New York, 1962.
  16. Sidon, S., Verallgemeinerung eines Satzes über die absolute Konvergenz von Fourierreihen mit Lücken, Math. Ann. 97 (1927), 675-676.
  17. Stechkin, S.B., On absolute convergence of Fourier series III, Izv. Akad. Nauk SSSR Ser. Mat. 20 (1956), 385-412 (in Russian).
  18. Wilson, D., On the structure of Sidon sets, Monatsh. Math. 101 (1986), 67-74.
Pages:
1-7
Main language of publication
English
Received
1999-03-01
Published
2000
Exact and natural sciences