Questions tagged [noncompact]

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8 votes
1 answer
224 views

Measure support decomposition that "tends to infinity"

I would like to know the answers to the following two questions. Let $S$ be a locally compact Hausdorff space, $\mu$ be a regular Borel measure with non-compact support $M$. Denote $$ \mathscr{H}=\{\...
Norbert's user avatar
  • 1,687
4 votes
0 answers
125 views

Pushforward of invariant measures (equivariant Moser theorem)

There is a well-known theorem that between any two absolutely continuous Borel probability measures $\mu$ and $\nu$ on $\mathbb{R}^n$ there is an increasing triangular transformation $T : \mathbb{R}^n ...
ivan's user avatar
  • 41
3 votes
1 answer
555 views

Compact dual of a noncompact Lie group

Let $\mathfrak{g}_0$ be a noncompact simple Lie algebra, and fix a Cartan involution $\theta$ of $\mathfrak{g}_0$, which gives a Cartan decomposition $\mathfrak{g}_0=\mathfrak{k}_0+\mathfrak{p}_0$. ...
Hebe's user avatar
  • 821
3 votes
1 answer
124 views

Totally minimal homeomorphisms on connected locally compact noncompact spaces

If $\alpha : X \to X$ is a minimal homeomorphism on a compact Hausdorff space $X$, then if $X$ is connected, $\alpha$ is totally minimal, that is $\alpha^k$ is minimal for every $k \in \mathbb{Z}$. I ...
Nimhiuil Feileacan's user avatar
3 votes
1 answer
114 views

Embed exceptional non-compact simply connected simple Lie groups into classical simple Lie groups with preserving centers

It is well known that there are exactly 22 exceptional simple real Lie algebras (5 compact, 5 split, 5 complex and 7 others). To each of these algebras there corresponds a unique simply connected (...
Piotr's user avatar
  • 31
3 votes
0 answers
114 views

Extension of Schur-Weyl duality for principal series in $SL(2, \mathbb{R})$

In the case of $SU(N)$ all unitary irreps can be obtained from reducing tensor products ($V^{\otimes n}$) of the fundamental representation ($V$). Then given the set of all $SU(N)$ Young diagrams with ...
Luca Iliesiu's user avatar
2 votes
2 answers
306 views

Unitary representations of SO(1,4) and SO(2,3)

Where can I find details about the irreducible unitary representations of SO(1,4) and SO(2,3)?
Arnold Neumaier's user avatar
2 votes
1 answer
157 views

Li-Yorke chaos: the non compact case

1) Is there any notion of Li-Yorke chaos for non compact (metric) spaces $X$ and non continuous transformation $f:X \rightarrow X$? Could you bring some references? 2) I mean, why are so important ...
Bruno Brogni Uggioni's user avatar
1 vote
1 answer
117 views

A neighborhood $Y$ of a set $X$ such that the line segment connecting any point in $Y$ and its projection to $X$ is contained in $Y$

A direct line from a point $p$ to a set $X$ is a line segment with one endpoint at $p$ and one endpoint in $X$, which is as short as any other line segment from $p$ to $X$. Given a closed set $X$ and ...
ccriscitiello's user avatar