Lacunary series on compact groups

Katherine Adams; David Grow

Colloquium Mathematicae (2000)

  • Volume: 86, Issue: 1, page 1-7
  • ISSN: 0010-1354

Abstract

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

How to cite

top

Adams, Katherine, and Grow, David. "Lacunary series on compact groups." Colloquium Mathematicae 86.1 (2000): 1-7. <http://eudml.org/doc/210837>.

@article{Adams2000,
abstract = {A theorem of Sidon concerning absolutely convergent Fourier series is extended to compact groups.},
author = {Adams, Katherine, Grow, David},
journal = {Colloquium Mathematicae},
keywords = {lacunary Fourier series; compact group; Sidon theorem; randomly continuous},
language = {eng},
number = {1},
pages = {1-7},
title = {Lacunary series on compact groups},
url = {http://eudml.org/doc/210837},
volume = {86},
year = {2000},
}

TY - JOUR
AU - Adams, Katherine
AU - Grow, David
TI - Lacunary series on compact groups
JO - Colloquium Mathematicae
PY - 2000
VL - 86
IS - 1
SP - 1
EP - 7
AB - A theorem of Sidon concerning absolutely convergent Fourier series is extended to compact groups.
LA - eng
KW - lacunary Fourier series; compact group; Sidon theorem; randomly continuous
UR - http://eudml.org/doc/210837
ER -

References

top
  1. [0] Adams, K., Weighted Sidon sets, Ph.D. dissertation, Univ. of Missouri at Rolla, 1998. 
  2. [1] Cecchini, C., Lacunary Fourier series on compact Lie groups, J. Funct. Anal. 11 (1972), 191-203. Zbl0246.43009
  3. [2] Banach, S., Über einige Eigenschaften der lakunären trigonometrischen Reihen, Studia Math. 2 (1930), 207-220. Zbl56.0941.03
  4. [3] Figà-Talamanca, A. and D. Rider, A theorem of Littlewood and lacunary series for compact groups, Pacific J. Math. 16 (1966), 505-514. Zbl0142.10501
  5. [4] Hare, K. and D. Wilson, Weighted p-Sidon sets, J. Austral. Math. Soc. 61 (1996), 73-95. Zbl0874.43005
  6. [5] Hewitt, E. and K. A. Ross, Abstract Harmonic Analysis, Vols. I and II, 2nd ed., Springer, New York, 1979. 
  7. [6] Hewitt, E. and H. S. Zuckerman, Some theorems on lacunary series with extensions to compact groups, Trans. Amer. Math. Soc. 93 (1959), 1-19. Zbl0141.12601
  8. [7] Hutchinson, M.F., Non-tall compact groups admit infinite Sidon sets, J. Austral. Math. Soc. 23 (1977), 467-475. Zbl0368.43005
  9. [8] López, J.H. and K. A. Ross, Sidon Sets, Marcel Dekker, New York, 1975. 
  10. [9] Marcus, M.B. and G. Pisier, Random Fourier Series with Applications to Harmonic Analysis, Princeton Univ. Press, Princeton, 1981. Zbl0474.43004
  11. [10] 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. [11] Rider, D., Gap series on groups and spheres, Canad. J. Math. 18 (1966), 389-398. Zbl0141.12602
  13. [12] Rider, D., Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), 759-764. Zbl0345.43008
  14. [13] Rudin, W., Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203-208. Zbl0091.05802
  15. [14] Rudin, W., Fourier Analysis on Groups, Wiley, New York, 1962. 
  16. [15] Sidon, S., Verallgemeinerung eines Satzes über die absolute Konvergenz von Fourierreihen mit Lücken, Math. Ann. 97 (1927), 675-676. Zbl53.0252.02
  17. [16] Stechkin, S.B., On absolute convergence of Fourier series III, Izv. Akad. Nauk SSSR Ser. Mat. 20 (1956), 385-412 (in Russian). Zbl0074.29104
  18. [17] Wilson, D., On the structure of Sidon sets, Monatsh. Math. 101 (1986), 67-74. Zbl0578.43007

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.