Lacunary series on compact groups

• Autorzy: Katherine Adams , David Grow
• Języki publikacji: EN

Abstrakty

EN

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2000
• Tom: 86
• Numer: 1
• Strony: 1-7

Daty

wydano

2000

otrzymano

1999-03-01

Twórcy

autor

Katherine Adams

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

autor

David Grow

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

Bibliografia

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