Sidon sets and Riesz sets for some measure algebras on the disk

• Autorzy: Olivier Gebuhrer , Alan L. Schwartz
• Języki publikacji: EN

Abstrakty

EN

Sidon sets for the disk polynomial measure algebra (the continuous disk polynomial hypergroup) are described completely in terms of classical Sidon sets for the circle; an analogue of the F. and M. Riesz theorem is also proved.

Słowa kluczowe

EN

disk polynomials   bivariate polynomials   Riesz sets   hypergroups   Sidon sets  

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 1997
• Tom: 72
• Numer: 2
• Strony: 269-279

Daty

wydano

1997

otrzymano

1995-08-30

poprawiono

1996-04-22

Twórcy

autor

Olivier Gebuhrer

• Département de Mathématique, Institut de Recherche Mathématique Avancée, Université Louis Pasteur, 67100 Strasbourg, France

autor

Alan L. Schwartz

• Department of Mathematics and Computer Science, University of Missouri-St. Louis, St. Louis, Missouri 63121, U.S.A.

Bibliografia

• [AT74] H. Annabi et K. Trimèche, Convolution généralisée sur le disque unité, C. R. Acad. Sci. Paris 278 (1974), 21-24.
• [BG91] M. Bouhaik and L. Gallardo, A Mehler-Heine formula for disk polynomials, Indag. Math. 1 (1991), 9-18.
• [BG92] M. Bouhaik and L. Gallardo, Un théorème limite central dans un hypergroupe bidimensionnel, Ann. Inst. H. Poincaré 28 (1992), 47-61.
• [BH95] W. R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, de Gruyter Stud. Math. 20, de Gruyter, Berlin, New York, 1995.
• [CS92] W. C. Connett and A. L. Schwartz, Fourier analysis off groups, in: The Madison Symposium on Complex Analysis (Providence, R.I.), A. Nagel and L. Stout (eds.), Contemp. Math. 137, Amer. Math. Soc. 1992, 169-176.
• [CS95] W. C. Connett and A. L. Schwartz, Continuous 2-variable polynomial hypergroups, in: Applications of Hypergroups and Related Measure Algebras (Providence, R.I.), O. Gebuhrer, W. C. Connett and A. L. Schwartz (eds.), Contemp. Math. 183, Amer. Math. Soc., 1995, 89-109.
• [Edw67] R. E. Edwards, Fourier Series, Vols. I, II, Holt, Rinehart and Winston, New York, 1967.
• [HK93] H. Heyer and S. Koshi, Harmonic Analysis on the Disk Hypergroup, Mathematical Seminar Notes, Tokyo Metropolitan University, 1993.
• [Kan76] Y. Kanjin, A convolution measure algebra on the unit disc, Tôhoku Math. J. (2) 28 (1976), 105-115.
• [Kan85] Y. Kanjin, Banach algebra related to disk polynomials, ibid. 37 (1985), 395-404.
• [Koo72] T. H. Koornwinder, The addition formula for Jacobi polynomials, II, the Laplace type integral representation and the product formula, Tech. Report TW 133/72, Mathematisch Centrum, Amsterdam, 1972.
• [Koo78] T. H. Koornwinder, Positivity proofs for linearization and connection coefficients of orthogonal polynomials satisfying an addition formula, J. London Math. Soc. (2) 18 (1978), 101-114.
• [Rud62] W. Rudin, Fourier Analysis on Groups, Interscience Publishers, 1962.
• [Sze67] G. Szegő, Orthogonal Polynomials, 2nd ed., Colloq. Publ. 23, Amer. Math. Soc., Providence, R.I., 1967.