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On weak spectral synthesis

Published online by Cambridge University Press:  17 April 2009

K. Parthasarathy  and
Sujatha Varma
K. Parthasarathy
Affiliation:
Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Madras - 600 005, India
Sujatha Varma
Affiliation:
Indira Gandhi National Open University, New Delhi, India
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Abstract

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Weak spectral synthesis fails in the group algebra and the generalised group algebra of any non compact locally compact abelian group and also in the Fourier algebra of any infinite compact Lie group.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 279 - 282
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Bloom, W.R., ‘Sets of p−spectral synthesis’, Pacific J. Math. 60 (1975), 7–19.CrossRefGoogle Scholar
[2]Hewitt, E. and Ross, K.A., Abstract Harmonic Analysis II (Springer-Verlag, Berlin, Heidelberg, New York, 1970).Google Scholar
[3]Johnson, G.P., ‘Spaces of functions with values in a Banach algebra’, Trans. Amer. Math. Soc. 92 (1959), 411–429.CrossRefGoogle Scholar
[4]Reiter, H., Classical Harmonic Analysis and Locally Compact Groups (Oxford University Press, Oxford, 1968).Google Scholar
[5]Rudin, W., Fourier Analysis on Groups (Interscience, New York, 1962).Google Scholar
[6]Varopoulos, N. Th., ‘Spectral synthesis on spheres’, Proc. Camb. Phil. Soc. 62 (1966), 379–387.CrossRefGoogle Scholar
[7]Warner, C.R., ‘Weak spectral synthesis’, Proc. Amer. Math. Soc. 99 (1987), 244–247.CrossRefGoogle Scholar