scholarly journals Quantization maps, algebra representation, and non-commutative Fourier transform for Lie groups

2013 ◽  
Vol 54 (8) ◽  
pp. 083508 ◽  
Author(s):  
Carlos Guedes ◽  
Daniele Oriti ◽  
Matti Raasakka
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Quantization Maps ◽  
Algebra Representation

Hardy's Theorem for simply connected nilpotent Lie groups

2001 ◽  
Vol 131 (3) ◽  
pp. 487-494 ◽  
Author(s):  
EBERHARD KANIUTH ◽  
AJAY KUMAR
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Nilpotent Lie Groups ◽  
Heisenberg Groups ◽  
Hardy’S Theorem ◽  
Simply Connected

We prove an analogue of Hardy's Theorem for Fourier transform pairs in ℝ for arbitrary simply connected nilpotent Lie groups, thus extending earlier work on ℝn and the Heisenberg groups ℍn.

The Duflo non-commutative Fourier transform for the Lorentz group

2020 ◽  
Vol 17 (supp01) ◽  
pp. 2040011
Author(s):  
Giacomo Rosati
Keyword(s):  
Fourier Transform ◽  
Phase Space ◽  
Quantum System ◽  
Lie Group ◽  
Lorentz Group ◽  
Commutative Algebra ◽  
Cotangent Bundle ◽  
Irreducible Representations ◽  
Algebra Representation

For a quantum system whose phase space is the cotangent bundle of a Lie group, like for systems endowed with particular cases of curved geometry, one usually resorts to a description in terms of the irreducible representations of the Lie group, where the role of (non-commutative) phase space variables remains obscure. However, a non-commutative Fourier transform can be defined, intertwining the group and (non-commutative) algebra representation, depending on the specific quantization map. We discuss the construction of the non-commutative Fourier transform and the non-commutative algebra representation, via the Duflo quantization map, for a system whose phase space is the cotangent bundle of the Lorentz group.

Estimate of the L p -Fourier Transform Norm on Strong ✱-Regular Exponential Solvable Lie Groups

2006 ◽  
Vol 23 (7) ◽  
pp. 1173-1188 ◽  
Author(s):  
A. Baklouti ◽  
J. Ludwig ◽  
L. Scuto ◽  
K. Smaoui
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Solvable Lie Groups

scholarly journals A qualitative uncertainty principle for semisimple Lie groups

1988 ◽  
Vol 45 (1) ◽  
pp. 127-132 ◽  
Author(s):  
Michael Cowling ◽  
John F. Price ◽  
Alladi Sitaram
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Uncertainty Principle ◽  
Finite Measure ◽  
Semisimple Lie Groups ◽  
Qualitative Uncertainty

AbstractRecently M. Benedicks showed that if a function f ∈ L2(Rd) and its Fourier transform both have supports of finite measure, then f = 0 almot everywhere. In this paper we give a version of this result for all noncompact semisimple connected Lie groups with finite centres.

scholarly journals VARIANTS OF MIYACHI’S THEOREM FOR NILPOTENT LIE GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 1-17 ◽  
Author(s):  
ALI BAKLOUTI ◽  
SUNDARAM THANGAVELU
Keyword(s):  
Fourier Transform ◽  
Lie Groups ◽  
Lie Group ◽  
Nilpotent Lie Groups ◽  
Nilpotent Lie Group ◽  
Group Fourier Transform ◽  
Simply Connected ◽  
Miyachi’S Theorem

AbstractWe formulate and prove two versions of Miyachi’s theorem for connected, simply connected nilpotent Lie groups. This allows us to prove the sharpness of the constant 1/4 in the theorems of Hardy and of Cowling and Price for any nilpotent Lie group. These theorems are proved using a variant of Miyachi’s theorem for the group Fourier transform.

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