Lacunary series on compact groups
Adams, Katherine ; Grow, David
Colloquium Mathematicae, Tome 84/85 (2000), p. 1-7 / Harvested from The Polish Digital Mathematics Library
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A theorem of Sidon concerning absolutely convergent Fourier series is extended to compact groups.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:210837 
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     title = {Lacunary series on compact groups},
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     volume = {84/85},
     year = {2000},
     pages = {1-7},
     zbl = {0965.43003},
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Adams, Katherine; Grow, David. Lacunary series on compact groups. Colloquium Mathematicae, Tome 84/85 (2000) pp. 1-7. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv86i1p1bwm/

[000] [0] Adams, K., Weighted Sidon sets, Ph.D. dissertation, Univ. of Missouri at Rolla, 1998.

[001] [1] Cecchini, C., Lacunary Fourier series on compact Lie groups, J. Funct. Anal. 11 (1972), 191-203. | Zbl 0246.43009

[002] [2] Banach, S., Über einige Eigenschaften der lakunären trigonometrischen Reihen, Studia Math. 2 (1930), 207-220. | Zbl 56.0941.03

[003] [3] Figà-Talamanca, A. and D. Rider, A theorem of Littlewood and lacunary series for compact groups, Pacific J. Math. 16 (1966), 505-514. | Zbl 0142.10501

[004] [4] Hare, K. and D. Wilson, Weighted p-Sidon sets, J. Austral. Math. Soc. 61 (1996), 73-95. | Zbl 0874.43005

[005] [5] Hewitt, E. and K. A. Ross, Abstract Harmonic Analysis, Vols. I and II, 2nd ed., Springer, New York, 1979.

[006] [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. | Zbl 0141.12601

[007] [7] Hutchinson, M.F., Non-tall compact groups admit infinite Sidon sets, J. Austral. Math. Soc. 23 (1977), 467-475. | Zbl 0368.43005

[008] [8] López, J.H. and K. A. Ross, Sidon Sets, Marcel Dekker, New York, 1975.

[009] [9] Marcus, M.B. and G. Pisier, Random Fourier Series with Applications to Harmonic Analysis, Princeton Univ. Press, Princeton, 1981. | Zbl 0474.43004

[010] [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.

[011] [11] Rider, D., Gap series on groups and spheres, Canad. J. Math. 18 (1966), 389-398. | Zbl 0141.12602

[012] [12] Rider, D., Randomly continuous functions and Sidon sets, Duke Math. J. 42 (1975), 759-764. | Zbl 0345.43008

[013] [13] Rudin, W., Trigonometric series with gaps, J. Math. Mech. 9 (1960), 203-208. | Zbl 0091.05802

[014] [14] Rudin, W., Fourier Analysis on Groups, Wiley, New York, 1962.

[015] [15] Sidon, S., Verallgemeinerung eines Satzes über die absolute Konvergenz von Fourierreihen mit Lücken, Math. Ann. 97 (1927), 675-676. | Zbl 53.0252.02

[016] [16] Stechkin, S.B., On absolute convergence of Fourier series III, Izv. Akad. Nauk SSSR Ser. Mat. 20 (1956), 385-412 (in Russian). | Zbl 0074.29104

[017] [17] Wilson, D., On the structure of Sidon sets, Monatsh. Math. 101 (1986), 67-74. | Zbl 0578.43007