scholarly journals GABOR ANALYSIS, NONCOMMUTATIVE TORI AND FEICHTINGER'S ALGEBRA

2007 ◽  
pp. 77-106 ◽  
Author(s):  
Franz Luef
Keyword(s):  
Noncommutative Tori ◽  
Gabor Analysis

scholarly journals Solitons of general topological charge over noncommutative tori

2020 ◽  
pp. 2150009
Author(s):  
Ludwik Da̧browski ◽  
Mads S. Jakobsen ◽  
Giovanni Landi ◽  
Franz Luef
Keyword(s):  
Topological Charge ◽  
Vector Bundles ◽  
Energy Functional ◽  
Gabor Frames ◽  
Noncommutative Tori ◽  
Gabor Analysis ◽  
Time Frequency ◽  
Moyal Plane ◽  
Higher Rank ◽  
Vector Valued

We study solitons of general topological charge over noncommutative tori from the perspective of time-frequency analysis. These solitons are associated with vector bundles of higher rank, expressed in terms of vector-valued Gabor frames. We apply the duality theory of Gabor analysis to show that Gaussians are such solitons for any value of a topological charge. Also they solve self/anti-self duality equations resulting from an energy functional for projections over noncommutative tori, and have a reformulation in terms of Gabor frames. As a consequence, the projections generated by Gaussians minimize the energy functional. We also comment on the case of the Moyal plane and the associated continuous vector-valued Gabor frames and show that Gaussians are the only class of solitons there.

Gabor Analysis on Wiener Amalgams

2007 ◽  
Vol 6 (2) ◽  
pp. 129-150
Author(s):  
Hans G. Feichtinger ◽  
Ferenc Weisz
Keyword(s):  
Gabor Analysis

scholarly journals Wilson lines on noncommutative tori

2000 ◽  
Vol 482 (1-3) ◽  
pp. 271-275 ◽  
Author(s):  
Anton Yu. Alekseev ◽  
Andrei G. Bytsko
Keyword(s):  
Noncommutative Tori

scholarly journals Gabor analysis as contraction of wavelets analysis

2017 ◽  
Vol 58 (8) ◽  
pp. 081702 ◽  
Author(s):  
Eyal M. Subag ◽  
Ehud Moshe Baruch ◽  
Joseph L. Birman ◽  
Ady Mann
Keyword(s):  
Gabor Analysis ◽  
Wavelets Analysis

New efficient methods for Gabor analysis

1993 ◽  
Author(s):  
Hans G. Feichtinger ◽  
Ole Christensen
Keyword(s):  
Gabor Analysis

Group theoretical approach to Gabor analysis

1995 ◽  
Vol 34 (6) ◽  
pp. 1697 ◽  
Author(s):  
Hans G. Feichtinger
Keyword(s):  
Theoretical Approach ◽  
Gabor Analysis
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