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Local Central Λ(p) Dual Objects

Published online by Cambridge University Press:  20 November 2018

Willard A. Parker
Willard A. Parker*
Affiliation:
Department of Mathematics Cardwell Hall Kansas State University, Manhattan, Kansas 66506
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The dual object T of a compact group is called a local central A(p) set if there is a constant K such that ‖X‖P < K ‖X‖1 for all irreducible characters X of G. For each γ∊Γ, Dr is an irreducible representation of G of dimension dγ. Several authors [1, 2, 3, 4] have observed that Γ is a local central Λ(p) set for p<l provided sup{dγ:γ∊Γ}>∞, and some of them [2, 3] conjectured the converse. Cecchini [1] showed that Γ is not a local central Λ(4) set if G is a compact Lie group.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 20 , Issue 4 , 01 December 1977 , pp. 515
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Carlo, Cecchini, Lacunary Fourier series on compact Lie groups, J. Functional Anal. 11 (1972), 191-203.Google Scholar
2. Picardello, Massimo A., Random Fourier series on compact noncommutative groups, Canad. J. Math. 27 (1975), 1400-1407.Google Scholar
3. Price, J.F., Local Sidon sets and uniform convergence of Fourier Series, Israel J. Math. 17 (1974), 169-175.Google Scholar
4. Daniel, Rider, Norms of characters and central Λp sets for U(n), Springer Lecture Notes #266 (1971 Maryland Conference), pp. 287-294.Google Scholar