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Rudin-Shapiro sequences for arbitrary compact groups

Published online by Cambridge University Press:  09 April 2009

J. R. McMullen  and
J. F. Price
J. R. McMullen
Affiliation:
University of Sydney, Sydney, N.S.W. 2006, Australia
J. F. Price
Affiliation:
University of New South Wales, Kensington, N.S.W. 2033, Australia
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Abstract

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Let G be a compact group. A sequence of functions in L∞ (G) is said to be a Rudin-Shapiro sequence (briefly, an RS-sequence) if the following conditions hold: (1) (2) (3) The main purpose here is to prove the following theorem: Theorem: Theorem. Let G be an infinite compact group. Then G has an RS-sequence consisting of trigonometric polynomials.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 22 , Issue 4 , December 1976 , pp. 421 - 430
Copyright
Copyright © Australian Mathematical Society 1976

References

Bourbaki, N. (1963), Éléments de Mathématique: Intégration, Chap. 7–8 (Hermann, Paris, 1963).Google Scholar
Brainerd, B. and Edwards, R. E. (1966), ‘Linear operators which commute with translations, Part 1: representation theorems’, J. Austral. Math. Soc. 6, 289–327.CrossRefGoogle Scholar
Edwards, R. E. (1965), Functional Analysis: Theory and Applications (Holt, Rinehart and Winston, New York, 1965).Google Scholar
Edwards, R. E. and Price, J. F. (1970), ‘A naively constructive approach to boundedness principles, with applications to harmonic analysis’, Enseignement Maht. 16, 255–296.Google Scholar
Figà-Talamanca, A. and Gaudry, G. I. (1970), ‘Multipliers and sets of uniquences of Lp’, Michigan Math. J. 17, 179–191.CrossRefGoogle Scholar
Figà-Talamanca, A. and Price, J. F., (1972) ‘Applications of random fourier series over compact groups to Fourier multipliers’, Pacific J. Math. 43, 531–541.CrossRefGoogle Scholar
Figà-Talamanca, A. and Price, J. F. (1973), ‘Rudin-Shapiro sequences on compact groups’, Bull. Austral. Math. Soc. 8, 241–245.CrossRefGoogle Scholar
Gaudry, G. I. (1970), ‘Bad behaviour and inclusion results for multipliers of type (p, q)’, Pacific J. Math. 35, 83–94.CrossRefGoogle Scholar
Hewitt, E. and Ross, K. A. (1963 and 1970), Abstract Harmonic Analysis (Vols I and II, Springer-Verlag, Berlin, 1963 and 1970).Google Scholar
Mackey, G. W. (1951), ‘On induced representations of groups’, Amer. J. Math. 73, 576–592.CrossRefGoogle Scholar
MuMullen, J. R. (1974), ‘Compact torsion groups’ (Proceedings of the Second International Conference on the Theory of Groups, Lecture Notes in Mathematics No. 372, Springer-Verlag, Berlin, 1974).CrossRefGoogle Scholar
Zassenhaus, H. (1938), ‘Beweis eines Satzes über diskrete Gruppen’, Abh. Math. Sem. Univ. Hamburg 12, 289–312.CrossRefGoogle Scholar