The Bonnet Plancherel formula for normal monomial representations of exponential solvable Lie groups

2005 ◽  
Vol 17 (5) ◽  
Author(s):  
A. Ghorbel ◽  
H. Hamrouni ◽  
J. Ludwig ◽  
M. Selmi
Keyword(s):  
Lie Groups ◽  
Plancherel Formula ◽  
Solvable Lie Groups ◽  
Monomial Representations

Variants of Plancherel Formulas for Monomial Representations of Exponential Solvable Lie Groups

2021 ◽  
pp. 235-280
Author(s):  
Ali Baklouti ◽  
Hidenori Fujiwara ◽  
Jean Ludwig
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Monomial Representations

scholarly journals An explicit Plancherel formula for completely solvable Lie groups.

1991 ◽  
Vol 38 (1) ◽  
pp. 75-87 ◽  
Author(s):  
Bradley N. Currey
Keyword(s):  
Lie Groups ◽  
Plancherel Formula ◽  
Solvable Lie Groups

Monomial Representations of Discrete Type of Exponential Solvable Lie Groups

2021 ◽  
pp. 401-451
Author(s):  
Ali Baklouti ◽  
Hidenori Fujiwara ◽  
Jean Ludwig
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Monomial Representations ◽  
Discrete Type

Analysis of some monomial representations of exponential solvable lie groups

2006 ◽  
Vol 13 (4) ◽  
pp. 363-379 ◽  
Author(s):  
A. Baklouti ◽  
H. Hamrouni ◽  
F. Khlif
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Monomial Representations

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

scholarly journals Joseph Fourier 250thBirthday: Modern Fourier Analysis and Fourier Heat Equation in Information Sciences for the XXIst Century

Entropy ◽  
2019 ◽  
Vol 21 (3) ◽  
pp. 250
Author(s):  
Frédéric Barbaresco ◽  
Jean-Pierre Gazeau
Keyword(s):  
Fourier Analysis ◽  
Heat Equation ◽  
Harmonic Analysis ◽  
Lie Groups ◽  
Coherent States ◽  
Geometric Theory ◽  
Plancherel Formula ◽  
Group Representations ◽  
Modern Development ◽  
Xxist Century

For the 250th birthday of Joseph Fourier, born in 1768 at Auxerre in France, this MDPI special issue will explore modern topics related to Fourier analysis and Fourier Heat Equation. Fourier analysis, named after Joseph Fourier, addresses classically commutative harmonic analysis. The modern development of Fourier analysis during XXth century has explored the generalization of Fourier and Fourier-Plancherel formula for non-commutative harmonic analysis, applied to locally compact non-Abelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups (by associating coherent states to group representations that are square integrable over a homogeneous space). The name of Joseph Fourier is also inseparable from the study of mathematics of heat. Modern research on Heat equation explores geometric extension of classical diffusion equation on Riemannian, sub-Riemannian manifolds, and Lie groups. The heat equation for a general volume form that not necessarily coincides with the Riemannian one is useful in sub-Riemannian geometry, where a canonical volume only exists in certain cases. A new geometric theory of heat is emerging by applying geometric mechanics tools extended for statistical mechanics, for example, the Lie groups thermodynamics.

scholarly journals Lattices of some solvable Lie groups and actions of products of affine groups

2009 ◽  
Vol 61 (3) ◽  
pp. 349-364 ◽  
Author(s):  
Nobuo Tsuchiya ◽  
Aiko Yamakawa
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Affine Groups

Analysis of a Distinguished Laplacian on Solvable Lie Groups

1993 ◽  
Vol 163 (1) ◽  
pp. 151-162 ◽  
Author(s):  
Saverio Giulini ◽  
Giancarlo Mauceri
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups
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