Gröchenig, K. Romero, J. L. Rottensteiner, D. Van Velthoven, J. T.
Published in
Analysis Mathematica

We prove strict necessary density conditions for coherent frames and Riesz sequences on homogeneous groups. Let N be a connected, simply connected nilpotent Lie group with a dilation structure (a homogeneous group) and let (π,Hπ) be an irreducible, square-integrable representation modulo the center Z(N) of N on a Hilbert space Hπ of formal dimensio...

Khanmohammadi, Ehssan
Published in
Mathematical Physics, Analysis and Geometry

We give a direct proof for the positivity of Kirillov’s character on the convolution algebra of smooth, compactly supported functions on a connected, simply connected nilpotent Lie group G. Then we use this positivity result to construct a representation of G × G and establish a G × G-equivariant isometric isomorphism between our representation and...

Lin, Ying-Fen Ludwig, Jean Molitor-Braun, Carine
Published in
Journal of Fourier Analysis and Applications

We establish a Fourier inversion theorem for general connected, simply connected nilpotent Lie groups G=exp(g)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G= \hbox {...

Wolf, JA

We examine the structure of the Levi component MA in a minimal parabolic subgroup P= MAN of a real reductive Lie group G and work out the cases where M is metabelian, equivalently where p is solvable. When G is a linear group we verify that p is solvable if and only if M is commutative. In the general case M is abelian modulo the center ZG , we ind...

Abdelmoula, Lobna Baklouti, Ali Bouaziz, Yasmine
Published in
Advances in Pure and Applied Mathematics

Let G be a type 1 connected and simply connected solvable Lie group. The generalized moment map for π in G^{\widehat{G}}, the unitary dual of G, sends smooth vectors of the representation space of π to 𝒰(𝔤)*{{\mathcal{U}(\mathfrak{g})}^{*}}, the dual vector space of 𝒰(𝔤){\mathcal{U}(\mathfrak{g})}. The convex hull of the image of the generalized ...

Beltiţă, Ingrid Ludwig, Jean
Published in
Mathematische Zeitschrift

We determine the space of primary ideals in the group algebra L1(G)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{1}(G) $$\end{document} of a connected nilpotent Li...

Arnal, Didier Currey, Bradley Oussa, Vignon
Published in
Monatshefte für Mathematik

Let V be a finite dimensional real vector space, let g\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathfrak g$$\end{document} be the real span of a finite set of co...

Poguntke, Detlev
Published in
Advances in Pure and Applied Mathematics

It was one of great successes of Kirillov's orbit method to see that the unitary dual of an exponential Lie group is in bijective correspondence with the orbit space associated with the linear dual of the Lie algebra of the group in question. To show that this correspondence is an homeomorphism turned out to be unexpectedly difficult. Only in 1994 ...

Baklouti, Ali Lahyani, Dhoha
Published in
Advances in Pure and Applied Mathematics

So far, the uncertainty principles for solvable non-exponential Lie groups have been treated only in few cases. The first author and Kaniuth produced an analogue of Hardy's theorem for a diamond Lie group, which is a semi-direct product of ℝd with the Heisenberg group ℍ 2d+1 ${\mathbb {H}_{2d+1}}$ In this setting, we formulate and prove in this pap...

Franco, Jose A.
Published in
European Journal of Mathematics

The classification of the Lie point symmetries of the nonlinear wave equations with dissipation give a generic case and eight special cases. In this article we show that in seven of the eight cases the action of the Lie symmetries can be globalized via induced representations of a family of solvable Lie groups. In one special case, we show that the...