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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
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Abstract

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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