2018/01/25 by Ludwik Dąbrowski, Mads S. Jakobsen, Dabrowski, Ludwik +5
Mathematics · Medicine · #Advanced Algebra and Geometry #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Glaucoma and retinal disorders #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Operator Algebras (math.OA)
paper · pdf · doi:10.48550/arxiv.1801.08596
openalex publication_date 2018/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue the study of solitons over noncommutative tori from the perspective of time-frequency analysis and treat the case of a general topological charge. Solutions are associated with vector bundles of higher rank over noncommutative tori. We express these vector bundles in terms of vector-valued Gabor frames and apply the duality theory of Gabor analysis to show that Gaussians are solitons of general topological charge over noncommutative tori. An energy functional for projections over noncommutative tori is the basis for the self and anti-self duality equations of the solitons which turns out to have a reformulation in terms of Gabor atoms and we prove that projections generated by Gaussians minimize this energy functional. Finally, we 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.