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$G$ be loacally compact abelian group with $G,\hat{G}$ both sigma compact. Let $f\in L^2(G)$ and $\psi_n(x)=\int_{C_n}\hat{f}(\chi)\chi(x)\ d\chi$.

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#fourier-analysis #fourier-transform #harmonic-analysis #topological-groups #locally-compact-groups
53
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Considering Haar integral as an element of an algebra

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#operator-algebras #c-star-algebras #von-neumann-algebras #locally-compact-groups
119
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Question concerning positive Weyl chamber

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#representation-theory #lie-groups #locally-compact-groups #semisimple-lie-algebras #weyl-group
175
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Topological semi-direct products

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#functional-analysis #topological-groups #locally-compact-groups
121
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Is assigning the central character a quotient map?

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#general-topology #representation-theory #harmonic-analysis #topological-groups #locally-compact-groups
50
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Group action on a topological space and Haar integral (A question on a proof in a Palais' paper)

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#integration #group-actions #locally-compact-groups #haar-measure
119
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Help with direct integral decomposition for locally compact groups

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#functional-analysis #representation-theory #locally-compact-groups
50
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Characterisation of subgroups that give compact quotients

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#locally-compact-groups
167
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If a monothetic group is locally compact, then it is either discrete or compact

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#general-topology #compactness #topological-groups #locally-compact-groups
32
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Why the addition group of a local field is isomorphic to its character group?

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#number-theory #topological-groups #local-field #locally-compact-groups
92
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Why does "Any bounded sequence $(x_n)⊂H$ contains a sub-sequence $(x_{n_k} )$ such that $(Cx_{n_k} )$ converges."?

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#general-topology #metric-spaces #hilbert-spaces #compact-operators #locally-compact-groups
78
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Does the vanishing of $\mathrm{Ext}^i_G(\rho,\pi)$ for every irreducible $\pi$ implies the same vanishing for more general representations $\pi$?

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#representation-theory #p-adic-number-theory #locally-compact-groups #profinite-groups
69
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Why are (Hausdorff) locally compact groups interesting?

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#soft-question #fourier-analysis #topological-groups #locally-compact-groups

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