Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-18T01:22:42.622Z Has data issue: false hasContentIssue false
  • English
  • Français

Lacunary sets for groups and hypergroups

Part of: Compact groups

Published online by Cambridge University Press:  09 April 2009

Catherine Finet
Catherine Finet
Affiliation:
Université de MonsFaculté des Sciences Avenue Maistriau 15 B 7000 Mons Belgique
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, we generalize the classical F. and M. Riesz theorem to compact groups and compact commutative hypergroups. The group SU(2) of unitary matrices is also studied.

MSC classification

Secondary: 22C05: Compact groups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 54 , Issue 1 , February 1993 , pp. 39 - 60
Copyright
Copyright © Australian Mathematical Society 1993

References

[1]Bachelis, G. F. and Ebenstein, S. E., ‘On Λ(p)-sets’ Pacific J. Math. 54 (1974), 35–38.Google Scholar
[2]Boclé, J., ‘Sur la théorie ergodique’, Ann. Inst. Fourier (Grenoble) 10 (1960), 1–45.Google Scholar
[3]Brummelhuis, R. G. M., ‘An F. and M. Riesz theorem for bounded symmetric domains’, Ann. Inst. Fourier (Grenoble) 37 (1987), 139–150.CrossRefGoogle Scholar
[4]Brummelhuis, R. G. M., ‘Variations on a theme of Frederic and Marcel Riesz’, Thesis.Google Scholar
[5]Brummelhuis, R. G. M., ‘A note on Riesz sets and lacunary sets’, J. Austral. Math. Soc. (Series A) 48 (1990), 57–65.Google Scholar
[6]Diestel, J., Geometry of Banach spaces. Selected topics, Lecture Notes in Math. 485 (Springer, Berlin, 1975).CrossRefGoogle Scholar
[7]Dressler, R. E. and Pigno, L., ‘Une remarque sur les ensembles de Rosenthal et Riesz’, Note aux C.R.A.S. 280 (1975), 1281–1282.Google Scholar
[8]Dunkl, C. F. and Ramirez, D. E., ‘A family of countable compact P*-hypergroups’, Trans. Amer. Math. Soc. 202 (1975), 338–356.Google Scholar
[9]Fournier, J. J. F. and Ross, K. A., ‘Random Fourier series on compact abelian hypergroups’, J. Austral. Math. Soc. (Series A) 37 (1984), 45–81.CrossRefGoogle Scholar
[10]Godefroy, G., ‘On Riesz subsets of abelian discrete groups’, Israel J. Math. 61 (1988), 301–331.CrossRefGoogle Scholar
[11]Godefroy, G., ‘On coanalytic families of sets in harmonic analysis’, Illinois J. Math. 35 (1991), 241–249.CrossRefGoogle Scholar
[12]Halmos, P., Measure theory (Van Nostrand, Princeton, 1950).CrossRefGoogle Scholar
[13]Havin, V. P., ‘Weak completeness of the space L1/H10’, Vestnik Leningard Univ. 13 (1973), 73–81 (in Russian).Google Scholar
[14]Hewitt, E. and Ross, K. A., Abstract: Harmonic Analysis II (Springer, Berlin, 1970).Google Scholar
[15]Jewett, R. I., ‘Spaces with an Abstract: convolution of measures’, Adv. Math. 18 (1975), 1–101.CrossRefGoogle Scholar
[16]Lust-Piquard, F., ‘Ensembles de Rosenthal et ensembles de Riesz’ C.R. Acad. Sci. Paris 282 (1976), 833–835.Google Scholar
[17]Meyer, Y., ‘Spectres des mesures et mesures absolument continues’, Studia Math. 30 (1968), 87–99.Google Scholar
[18]Mooney, M. C., ‘A theorem on bounded analytic functions’, Pacific J. Math. 43 (1972), 457–463.Google Scholar
[19]Price, J. F., ‘Non a sono inoemi infiniti di tipo Λ(p) per SU(2)’, Boll. Un. Mat. Ital. 4 (4) (1971), 879–881.Google Scholar
[20]Rider, D., ‘SU(n) has no infinite local Λp sets’, Boll. Un. Mat. Ital. 12 (4) (1975), 155–160.Google Scholar
[21]Rudin, W., Real and complex analysis (McGraw-Hill, New York, 1966).Google Scholar
[22]Shapiro, J., ‘Subspaces of Lp (G) spanned by characters, 0 < p < 1’, Israel J. Math. 29 (1978), 248–264.CrossRefGoogle Scholar
[23]Spector, R., ‘Aperçu de la théorie des hypergroupes’, in: Analyse harmonique sur les groupes de Lie. sém. Nancy-Strasbourg 1973–1975, Lecture Notes in Math. 497 (Springer, Berlin, 1976) pp. 643–673.Google Scholar
[24]Vrem, R. C., ‘Harmonic analysis on compact hypergroups’, Pacific J. Math. 85 (1979), 239–251.CrossRefGoogle Scholar