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1
Content available remote

The size of characters of compact Lie groups

100%
Hare K. E.
Studia Mathematica
|
1998
|
tom 129
|
nr 1
1-18
EN
Pointwise upper bounds for characters of compact, connected, simple Lie groups are obtained which enable one to prove that if μ is any central, continuous measure and n exceeds half the dimension of the Lie group, then $μ^n ∈ L^1$. When μ is a continuous, orbital measure then $μ^n$ is seen to belong to $L^2$. Lower bounds on the p-norms of characters are also obtained, and are used to show that, as in the abelian case, m-fold products of Sidon sets are not p-Sidon if p < 2m/(m+1).
2
Content available remote

Random weighted Sidon sets

100%
Hare K. E.
Colloquium Mathematicum
|
2000
|
tom 86
|
nr 1
103-109
EN
We investigate random Sidon-type sets in which the degrees of the representations are weighted. These variants of Sidon sets are of interest as there are compact non-abelian groups which admit no infinite Sidon sets. In this note we determine the largest weight function such that infinite random weighted Sidon sets exist in all infinite compact groups.
3
Content available remote

The size of $(L^2,L^p)$ multipliers

100%
Hare K. E.
Colloquium Mathematicum
|
1992
|
tom 63
|
nr 2
249-262
4
Content available remote

Sidonicity in compact, abelian hypergroups

100%
Hare K. E.
Colloquium Mathematicum
|
1998
|
tom 76
|
nr 2
171-180
5
Content available remote

The support of a function with thin spectrum

100%
Hare K. E.
Colloquium Mathematicum
|
1994
|
tom 67
|
nr 1
147-154
EN
We prove that if $E ⊆ Ĝ$ does not contain parallelepipeds of arbitrarily large dimension then for any open, non-empty $S ⊆ G$ there exists a constant c > 0 such that $∥ f1_S ∥_2 ≥ c ∥ f ∥ _2$ for all $f ∈ L^2(G)$ whose Fourier transform is supported on E. In particular, such functions cannot vanish on any open, non-empty subset of G. Examples of sets which do not contain parallelepipeds of arbitrarily large dimension include all Λ(p) sets.
6
Content available remote

Tame $L^p$-multipliers

100%
Hare K. E.
Colloquium Mathematicum
|
1993
|
tom 64
|
nr 2
303-314
EN
We call an $L^{p}$-multiplier m tame if for each complex homomorphism χ acting on the space of $L^{p}$ multipliers there is some $γ_{0} ∈ Γ$ and |a| ≤ 1 such that $χ(γm) = am(γ_{0}γ)$ for all γ ∈ Γ. Examples of tame multipliers include tame measures and one-sided Riesz products. Tame multipliers show an interesting similarity to measures. Indeed we show that the only tame idempotent multipliers are measures. We obtain quantitative estimates on the size of $L^{p}$-improving tame multipliers which are similar to those obtained for measures, but are false for non-tame multipliers. One-sided Riesz products are seen to play a similar role in the study of tame multipliers as Riesz products do in the study of measures.
7
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Strict-2-associatedness for thin sets

38%
Hare K. E.
Colloquium Mathematicum
|
1988
|
tom 56
|
nr 2
367-381
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