• Convolutions for Berezin quantization and Berezin-Lieb inequalities 

      Luef, Franz; Skrettingland, Eirik (Journal article; Peer reviewed, 2018)
      Concepts and results from quantum harmonic analysis, such as the convolution between functions and operators or between two operators, are identified as the appropriate setting for Berezin quantization and Berezin-Lieb ...
    • Convolutions for localization operators 

      Luef, Franz; Skrettingland, Eirik (Journal article; Peer reviewed, 2018)
      Quantum harmonic analysis on phase space is shown to be linked with localization operators. The convolution between operators and the convolution between a function and an operator provide a conceptual framework for the ...
    • Convolutions for Localization Operators 

      Skrettingland, Eirik (Master thesis, 2017)
      The theory of quantum harmonic analysis on phase space introduced by Werner is presented and formulated precisely using the terminology of time-frequency analysis and abstract harmonic analysis. Convolutions of functions ...
    • A Duality Principle for Groups II: Multi-frames Meet Super-Frames 

      Balan, Radu; Dutkay, Dorin; Han, Deguang; David, Larson; Luef, Franz (Peer reviewed; Journal article, 2020)
      The duality principle for group representations developed in Dutkay et al. (J Funct Anal 257:1133–1143, 2009), Han and Larson (Bull Lond Math Soc 40:685–695, 2008) exhibits a fact that the well-known duality principle in ...
    • Gabor duality theory for Morita equivalent C*-algebras 

      Austad, Are; Jakobsen, Mads Sielemann; Luef, Franz (Journal article; Peer reviewed, 2020)
      The duality principle for Gabor frames is one of the pillars of Gabor analysis. We establish a far-reaching generalization to Morita equivalence bimodules with some extra properties. For certain twisted group C∗-algebras, ...
    • Ikke-kommutative Sobolev-rom 

      Gulbrandsrud, Haakon Holm (Master thesis, 2017)
      Først blir det essensielle av forkunnskaper introdusert. Dette inneholder den grunnleggende Hilbert C*-modulteorien, definisjonen og konstruksjonen av Moritaekvivalenser samt noen konsekvenser av dette. På disse bimodulene ...
    • Metaplectic transformations and finite group actions on noncommutative tori 

      Chakraborty, Sayan; Luef, Franz (Journal article; Peer reviewed, 2019)
      In this article we describe extensions of some K-theory classes of Heisenberg modules over higher-dimensional noncommutative tori to projective modules over crossed products of non\-commutative tori by finite cyclic groups, ...
    • Mixed-State Localization Operators: Cohen’s Class and Trace Class Operators 

      Luef, Franz; Skrettingland, Eirik (Journal article; Peer reviewed, 2019)
      We study mixed-state localization operators from the perspective of Werner’s operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal ...
    • Noncommutative Geometry in Wireless Communication Applications 

      Nås, Sindre (Master thesis, 2018)
      The theory of time-frequency analysis is introduced, and basic results on modulation spaces are proved. We describe Gabor frames and prove results which are relevant to application in wireless communication. We outline a ...
    • Nonlinear phase unwinding 

      Jørgensen, Erik (Master thesis, 2018)
      We start of by studying Hardy spaces and Blaschke products. Then we look at a natural nonlinear analogue of Fourier series called the unwinding series. It is obtained through iterative Blaschke factorization and unwinds ...
    • On Accumulated Cohen's Class Distributions and Mixed-State Localization Operators 

      Luef, Franz; Skrettingland, Eirik (Journal article; Peer reviewed, 2019)
      Recently we introduced mixed-state localization operators associated with a density operator and a (compact) domain in phase space. We continue the investigations of their eigenvalues and eigenvectors. Our main focus is ...
    • Rational Noncommutative Tori and Gabor Frames 

      Enstad, Ulrik Bo Rufus (Master thesis, 2016)
      A link between noncommutative geometry and time-frequency analysis is used to show that the TKNN equation violates existence results for Gabor frames with atoms in the Schwartz space. In particular, we use that the Schwartz ...
    • Sampling and periodization of generators of Heisenberg modules 

      Jakobsen, Mads Sielemann; Luef, Franz (Journal article; Peer reviewed, 2019)
      This paper considers generators of Heisenberg modules in the case of twisted group C∗-algebras of closed subgroups of locally compact abelian (LCA) groups and how the restriction and/or periodization of these generators ...
    • Solitons of general topological charge over noncommutative tori 

      Dabrowski, Ludwik; Jakobsen, Mads Sielemann; Landi, Giovanni; Luef, Franz (Peer reviewed; Journal article, 2021)
      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 ...
    • The Algebraic Bivariant Connes-Chern Character 

      Austad, Are (Master thesis, 2017)
      In this thesis we present many properties of bivariant periodic cyclic homology with the purpose of then constructing two bivariant Connes-Chern characters from algebraic versions of Kasparov's KK-theory with values in ...
    • The Balian–Low theorem and noncommutative tori 

      Luef, Franz (Journal article; Peer reviewed, 2018)
      We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor–Riesz bases and a constant curvature connection on projective modules over noncommutative tori.
    • Time-frequency analysis on the adeles over the rationals 

      Enstad, Ulrik Bo Rufus; Jakobsen, Mads Sielemann; Luef, Franz (Journal article; Peer reviewed, 2019)
      We show that the construction of Gabor frames in with generators in and with respect to time-frequency shifts from a rectangular lattice is equivalent to the construction of certain Gabor frames for over the adeles over ...
    • Yang-Mills connections on quantum Heisenberg manifolds 

      Kang, Sooran; Luef, Franz; Judith, Packer (Journal article; Peer reviewed, 2020)
      We investigate critical points and minimizers of the Yang-Mills functional YM on quantum Heisenberg manifolds Dc µν, where the Yang-Mills functional is defined on the set of all compatible linear connections on finitely ...