All Questions
8 questions
8
votes
2
answers
1k
views
What does the unique mean on weakly almost periodic functions look like?
There is a unique invariant mean $m$ on WAP functions on any discrete group (see definitions below, theorem of ?). However, the proofs I found are fairly non-explicit on how to obtain this invariant ...
- 426
0
votes
1
answer
204
views
A certain class of representations
Let $g$ be a non-identity element in a torsion-free amenable group, does there exist a finite-dimensional unitary representation $\pi$ with $\pi(g)\neq 1$?
(The word "finite-dimensional" was ...
- 18.7k
3
votes
1
answer
213
views
About understanding manifold structure on WAP compactification of $\Bbb{C} \rtimes \Bbb{T}$
Let $G$ be a locally compact topological group. A continuous bounded function $f$ on $G$ is called (weakly) almost periodic if the set $L_Gf$ of left translates is relatively compact in the (weak) ...
- 2,391
2
votes
1
answer
172
views
Ideals of $L^1(G)$ and normal subgroups of $G$
Let $G$ be a locally compact group. Is there any correspondence between closed two-sided ideals of $L^1(G)$ and closed normal subgroups of $G$? (Especially, is there any correspondence between finite ...
- 25.8k
4
votes
0
answers
114
views
Coming up with a represenation for sum of functions in the Fourier algebra
This is my first overflow question, so let me apologize in advance if this belongs on http://math.stackexchange.com.
Let $G$ be a discrete group.
Let $\lambda:G\to B(\ell^{2}(G))$ be the left ...
- 25.8k
4
votes
1
answer
495
views
Weil's Haar measure construction from below
Weil's construction of a Haar measure on a locally compact group rests on approximating a function from above by sums of translates of another function.
I would need to know something similar for an ...
- 11.6k
5
votes
1
answer
1k
views
Is every distribution a linear combination of Dirac deltas?
My question is whether Dirac-type distributions over an Abelian group define a basis of the Schwartz-Bruhat space $\mathcal{S}(G)^\times$ of tempered distributions on $G$, so that any distribution $f\...
3
votes
0
answers
301
views
What information about a locally compact group $G$ is encoded in $C_r^\ast(G)$ which is not in $L^1(G)$?
Let $G$ be a locally compact group and let $ C_r^\ast(G) $ denote its reduced group $C^\ast$-algebra. Many features of a $G$ can be realized from $L^1(G)$ or $C_r^\ast(G)$. For example, $G$ is ...
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