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Central lacunary sets for Lie groups

Published online by Cambridge University Press:  09 April 2009

A. H. Dooley
A. H. Dooley
Affiliation:
School of MathematicsUniversity of New South WalesP.O. Box 1, Kensington, N.S.W. 2033, Australia
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Abstract

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If G is a compact connected Lie group every infinite subset of Ĝ contains an infinite central Λ(p) set, for p < 2 + 2 rank G/(dim G - rank G). A subset R of Ĝ is of type central Λ(2) if and only if the associated set of characters on the maximal torus is of type Λ(2). The dual of a compact connected semisimple Lie group contains infinite sets which are central p-Sidon for all p > 1. Every infinite subset of the dual of Su(2) contains such a set.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 45 , Issue 1 , August 1988 , pp. 30 - 45
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Blei, R., ‘Combinatorial dimension and certain norms in harmonic analysis’, Amer. J. Math., to appear.Google Scholar
[2]Cartwright, D. and McMullen, J. R., ‘A structural criterion for the existence of infinite Sidon sets’, Pacific J. Math. 96 (1981), 301–317.CrossRefGoogle Scholar
[3]Dooley, A. H., ‘On lacunary sets for nonabelian groups’, J. Austral. Math. Soc. Ser. A 25 (1978), 167–175.Google Scholar
[4]Dooley, A. H. and Soardi, P. M., ‘Local p-Sidon sets for Lie groups’, Proc. Amer. Math. Soc. 72 (1978), 125–126.Google Scholar
[5]Edwards, R. E. and Ross, K. A., ‘p-Sidon sets’, J. Functional Anal. 15 (1974), 404–427.CrossRefGoogle Scholar
[6]Humphreys, J. E., Introduction to Lie algebras and representation theory (Springer-Verlag, Berlin, 1972).CrossRefGoogle Scholar
[7]Johnson, G. and Woodward, G. S., ‘On p-Sidon sets’, Indiana Univ. Math. J. 24 (1974/1975), 161–167.CrossRefGoogle Scholar
[8]Parker, W. A., ‘Central Sidon and central Λp sets’, J. Austral. Math. Soc. 14 (1972), 62–74.CrossRefGoogle Scholar
[9]Price, J. F., ‘Non ci sono insiemi di tipo Λp per SU(2)’, Boll. Un. Mat. Ital. (4) 4 (1971), 871–881.Google Scholar
[10]Rider, D., ‘Central lacunary sets’, Monatsh. Math. 76 (1972), 328–338.CrossRefGoogle Scholar
[11]Rider, D., ‘Norms of characters and central Λ(p) sets for U(n)’, (Lecture Notes in Mathematics 266, pp. 287–294, Springer-Verlag, Berlin and New York, 1972).Google Scholar
[12]Rider, D., ‘Su(n) has no infinite local Λp sets’ preprint.Google Scholar
[13]Rudin, W., ‘Trigonometric series with gaps’, J. Math. Mech. 9 (1960), 203–227.Google Scholar
[14]Sanders, J. W., ‘Weighted Sidon sets’, Pacific J. Math. 63 (1976), 225–279.Google Scholar
[15]Wallach, N. R., Harmonic analysis on homogeneous spaces (Marcel Dekker, New York, 1973).Google Scholar