Mixing
Showing continuity of a function defined as the integral of $chi mapsto chi(x)$ over the dual group $hat G$
$begingroup$
Let $G$ be a topological group. Let's assume $G$ is abelian, locally compact and Hausdorff. Then there exists is a Haar measure $d nu$ for $G$ and $d mu$ for $hat G$. Under the assumption that the total variation of $d mu$ is finite we can define
$$x mapsto int_{hat G} chi(x) dmu(chi)$$
as a function from $G$ to $mathbb C$. Can we show that this defines a continuous function?
functional-analysis continuity harmonic-analysis topological-groups
asked Jan 31 at 20:52
MuziMuzi
453320
$endgroup$
add a comment |
$begingroup$
Let $G$ be a topological group. Let's assume $G$ is abelian, locally compact and Hausdorff. Then there exists is a Haar measure $d nu$ for $G$ and $d mu$ for $hat G$. Under the assumption that the total variation of $d mu$ is finite we can define
$$x mapsto int_{hat G} chi(x) dmu(chi)$$
as a function from $G$ to $mathbb C$. Can we show that this defines a continuous function?
functional-analysis continuity harmonic-analysis topological-groups
asked Jan 31 at 20:52
MuziMuzi
453320
$endgroup$
add a comment |
$begingroup$
Let $G$ be a topological group. Let's assume $G$ is abelian, locally compact and Hausdorff. Then there exists is a Haar measure $d nu$ for $G$ and $d mu$ for $hat G$. Under the assumption that the total variation of $d mu$ is finite we can define
$$x mapsto int_{hat G} chi(x) dmu(chi)$$
as a function from $G$ to $mathbb C$. Can we show that this defines a continuous function?
functional-analysis continuity harmonic-analysis topological-groups
asked Jan 31 at 20:52
MuziMuzi
453320
$endgroup$
Let $G$ be a topological group. Let's assume $G$ is abelian, locally compact and Hausdorff. Then there exists is a Haar measure $d nu$ for $G$ and $d mu$ for $hat G$. Under the assumption that the total variation of $d mu$ is finite we can define
$$x mapsto int_{hat G} chi(x) dmu(chi)$$
as a function from $G$ to $mathbb C$. Can we show that this defines a continuous function?
functional-analysis continuity harmonic-analysis topological-groups
functional-analysis continuity harmonic-analysis topological-groups
asked Jan 31 at 20:52
MuziMuzi
453320
asked Jan 31 at 20:52
MuziMuzi
453320
asked Jan 31 at 20:52
MuziMuzi
453320
asked Jan 31 at 20:52
MuziMuzi
453320
asked Jan 31 at 20:52
MuziMuzi
453320
453320
add a comment |
add a comment |
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