All Questions
8 questions
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 ...
user1688
3
votes
1
answer
861
views
Continuous function defined by measurable sets
Is the following slightly generalization of Corollary 20.17 in Hewitt and Ross Book (page 296) correct?
Let $A$ be a subset of a profinite group $G$ ( compact, Hausdorff, totally disconnected ...
- 3,738
3
votes
1
answer
347
views
Subgroups of finite non-zero Haar measure of abelian locally compact groups
Is it true that every subgroup of finite non-zero Haar measure of an abelian locally compact group should be open and compact? This is obviously true for the case of discrete abelian groups. Thanks.
- 895
3
votes
0
answers
740
views
Justification of the convolution operation of $L^1(G)$ functions where $G$ is a LCA group (measurability)
Suppose $G$ is a locally compact abelian Hausdorff group (LCA), and $\lambda$ is the Haar measure on it. We all know the convolution of two $L^1(\lambda)$ functions $f$ and $g$ on $G$ is defined as
$$...
- 960
2
votes
1
answer
223
views
Show that $V_G: L^2(G\times G, \mu \times \mu)\to L^2(G\times G, \mu \times \mu)$ defined by $V_G(f)(x,y) = f(xy,y)$ is well-defined
Let $G$ be a locally compact Hausdorff group and let $\mu$ be a right Haar measure on $G$. Then $\mu\times \mu$ (the Radon product of measures) is a right Haar measure on $G \times G$ and we can ...
- 175
2
votes
0
answers
187
views
How can the maximal ideal space of the Fourier Stieltjes algebra be non-separable?
I have been asking a fair few (probably elementary) questions about abstract harmonic analysis lately. By means of explanation, I am just feeling around the subject at the moment and trying to build ...
- 1,955
2
votes
0
answers
435
views
Generalized conjugacy classes in (topological) groups
Let $G$ be a topological group. We define an equivalence relation on $G$ as follows:
For $a,b\in G$ we set $a\sim b$ if the following two maps are topologically conjugate:
$$x\mapsto ax,\qquad x\...
- 356
1
vote
0
answers
115
views
Can Gaussian measure be characterized by unitary representations?
It is well known that Fourier transform switches positive-definite functions with positive measures on a (locally compact topological) group. Further, the positive definite functions can be ...
- 6,259