Three results on I-sets

Graham, Colin C.; Ramsey, Thomas

doi:10.4064/cm-51-1-141-147

Cited by 4 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When G is abelian, the I 0 sets relate well to the Bohr compactification of G. For example, each I 0 set equals the intersection of its closure with G [5]. A persistent open problem is whether a Sidon set can be distinctly different in this regard: can there be a Sidon set that is dense in the Bohr compactification of G?…”

Section: Introduction and Historymentioning

confidence: 99%

$I_0$ sets in non-abelian groups

Hare

Ramsey

2003

Math. Proc. Camb. Phil. Soc.

View full text Add to dashboard Cite

For the dual object of any compact, non-abelian group, the theory of $I_0$ sets (sets of interpolation by Fourier transforms of discrete measures) is quite different from that for abelian compact groups. In general, infinite $I_0$ sets need not exist. However, when the dual object contains an infinite (local) Sidon set, we prove that this set itself has an infinite $I_0$ subset.The proof is constructive and includes some key examples of $I_0$ sets: certain sets of representations of bounded degree and, for products of simple Lie groups, the set of self-representations of the factor groups and their conjugates (the FTR sets).

show abstract

Section: Introduction and Historymentioning

confidence: 99%

$I_0$ sets in non-abelian groups

Hare

Ramsey

2003

Math. Proc. Camb. Phil. Soc.

View full text Add to dashboard Cite

show abstract

“…[11]), we may meaningfully speak about the restriction ϕ |Ĝ of ϕ toĜ. Clearly, ϕ |Ĝ is an odd function mappinĝ G \ (Ĝ) (2) into {−1, 1} and (Ĝ) (2) onto {0}.…”

Section: Characterising C-groups and Bc-groups: Sufficient Conditionsmentioning

confidence: 99%

Group representations of bounded cosine functions.

1996

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

View full text Add to dashboard Cite

Abstract. We characterise two classes of locally compact Abelian groups. One of these comprises all groups G such that every bounded continuous cosine function on G with values in a sequentially complete semitopological algebra with identity has a regular group representation. The other comprises all groups G such that every bounded continuous cosine function on G with values in a sequentially complete semitopological algebra with identity has a bounded regular group representation.

show abstract

Almost periodic functions and representations in locally convex spaces

Shtern¹

2005

Russ. Math. Surv.

View full text Add to dashboard Cite

Three results on I-sets

Cited by 4 publications

References 0 publications

$I_0$ sets in non-abelian groups

$I_0$ sets in non-abelian groups

Group representations of bounded cosine functions.

Almost periodic functions and representations in locally convex spaces

Contact Info

Product

Resources

About