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Questions tagged [haar-measure]

Use this tag for questions related to the Haar measure, which is an assignment of an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups.

The Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups.

Haar measures are used in analysis, number theory, group theory, representation theory, statistics, probability theory, and ergodic theory.

341 questions
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Integration of periodic functions on the real line with respect to the Haar measure of 1-dim. torus

A function $f:\mathbb R \to \mathbb C$ with period 1 can be identitied with a function defined on the 1-dimensional torus $\mathbb T = \mathbb R / \mathbb Z$, the latter being continuous if and only if $f$ is. The Lebesgue measure on $\mathbb R$ is…
Ulysse Keller
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How to write a Haar measure on $SO(n)$ and $SU(n)$ given Haar measure on $GL(n)$?

How to write a Haar measure on $\operatorname{SO}(n)$ and $\operatorname{SU}(n)$ given Haar measure on $\operatorname{GL}(n)\,$? I know that $\operatorname{GL}(n)$ has the Haar measure $(\det(A)^{-1} dA)$. I try to write from these a Haar measure…
Francisca
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Doubt on Haar intergrals

Let $(C,G,\alpha)$ be a $C^*$ dynamical system where $G$ is a locally compact Hausdorff topological group. and let $C_c(G,A)$ be the collection of compactly supported continuous functions from $G \to A$. Let $f,g \in C_c(G,A)$. Then I want to prove…
budi
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If $G/[G,G]$ is compact, then $G$ is unimodular.

How to prove Proposition 2.29 in page no. 52 of the book " A Course in Abstract Harmonic Analysis (2nd edition)" by G.B. Folland which states that: If $G/[G,G]$ is compact, then $G$ is unimodular. Note: A proof is provided but I am unable to grasp…
Prof.Hijibiji
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