Ulrik Bo Rufus Enstad

• Enstad, Ulrik Bo Rufus & Luef, Franz (2025). Bessel duality of Gabor systems: A von Neumann algebraic perspective. Expositiones mathematicae. ISSN 0723-0869. 43(6). doi: 10.1016/j.exmath.2025.125741. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus & Velthoven, Jordy Timo van (2025). Linear independence of coherent systems associated to discrete subgroups. Bulletin of the London Mathematical Society. ISSN 0024-6093. 57(2), s. 315–329. doi: 10.1112/blms.13226. Fulltekst i vitenarkiv Vis sammendrag

  This note considers the finite linear independence of coherent systems associated to discrete subgroups. We show by simple arguments that such coherent systems of amenable groups are linearly independent whenever the associated twisted group ring does not contain any nontrivial zero divisors. We verify the latter for discrete subgroups in nilpotent Lie groups. For the particular case of time-frequency translates of Euclidean space, our approach provides a simple and self-contained proof of the Heil–Ramanathan–Topiwala conjecture for subsets of arbitrary discrete subgroups.

• Enstad, Ulrik Bo Rufus & Velthoven, Jordy Timo Van (2025). Coherent systems over approximate lattices in amenable groups. Annales de l'Institut Fourier. ISSN 0373-0956. 75(6), s. 2293–2315. doi: 10.5802/aif.3687. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus & Raum, Sven (2024). A dynamical approach to sampling and interpolation in unimodular groups. Transactions of the American Mathematical Society. ISSN 0002-9947. 378(3), s. 1975–2006. doi: 10.1090/tran/9326. Fulltekst i vitenarkiv Vis sammendrag

  We introduce a notion of covolume for point sets in locally compact groups that simultaneously generalizes the covolume of a lattice and the reciprocal of the Beurling density for amenable, unimodular groups. This notion of covolume arises naturally from transverse measure theory applied to the hull dynamical system associated to a point set. Using groupoid techniques, we prove necessary conditions for sampling and interpolation in reproducing kernel Hilbert spaces of functions on unimodular groups in terms of this new notion of covolume. These conditions generalize previously known density theorems for compactly generated groups of polynomial growth, while also covering important new examples, in particular model sets arising from cut-and-project schemes.

• Enstad, Ulrik Bo Rufus; Vilalta, Eduard & Thiel, Hannes (2024). Criteria for the Existence of Schwartz Gabor Frames Over Rational Lattices. arXiv.org. ISSN 2331-8422. 2025(5), s. 1–12. doi: 10.1093/imrn/rnaf038. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus; Raum, Sven & Favre, Gabriel (2023). Free actions of polynomial growth Lie groups and classifiable C*-algebras. arXiv.org. ISSN 2331-8422. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus & Velthoven, Jordy Timo Van (2023). Linear independence of coherent systems associated to lattices. arXiv.org. ISSN 2331-8422. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus & Velthoven, Jordy Timo Van (2022). On sufficient density conditions for lattice orbits of relative discrete series. Archiv der Mathematik. ISSN 0003-889X. doi: 10.1007/s00013-022-01748-8. Fulltekst i vitenarkiv Vis sammendrag

  This note provides new criteria on a unimodular group G and a discrete series representation (π,Hπ) of formal degree dπ>0 under which any lattice Γ≤G with vol(G/Γ)dπ≤1 (resp. vol(G/Γ)dπ≥1) admits g∈Hπ such that π(Γ)g is a frame (resp. Riesz sequence). The results apply to all projective discrete series of exponential Lie groups.

• Bedos, Eric Christophe; Enstad, Ulrik Bo Rufus & Velthoven, Jordy Timo Van (2022). Smooth lattice orbits of nilpotent groups and strict comparison of projections. Journal of Functional Analysis. ISSN 0022-1236. 283(6). doi: 10.1016/j.jfa.2022.109572. Fulltekst i vitenarkiv Vis sammendrag

  This paper provides sufficient density conditions for the existence of smooth vectors generating a frame or Riesz sequence in the lattice orbit of a square-integrable projective representation of a nilpotent Lie group. The conditions involve the product of lattice co-volume and formal dimension, and complement Balian–Low type theorems for the non-existence of smooth frames and Riesz sequences at the critical density. The proof hinges on a connection between smooth lattice orbits and generators for an explicitly constructed finitely generated Hilbert C*-module. An important ingredient in the approach is that twisted group C*-algebras associated to finitely generated nilpotent groups have finite decomposition rank, hence finite nuclear dimension, which allows us to deduce that any matrix algebra over such a simple C*-algebra has strict comparison of projections.

• Enstad, Ulrik Bo Rufus (2022). The density theorem for projective representations via twisted group von Neumann algebras. Journal of Mathematical Analysis and Applications. ISSN 0022-247X. 511(2). doi: 10.1016/j.jmaa.2022.126072. Fulltekst i vitenarkiv Vis sammendrag

  We consider converses to the density theorem for square-integrable, irreducible, projective, unitary group representations restricted to lattices using the dimension theory of Hilbert modules over twisted group von Neumann algebras. We show that the restriction of such a σ-projective unitary representation πof a unimodular, second-countable group G to a lattice Γ extends to a Hilbert module over the twisted group von Neumann algebra of (Γ, σ). We then compute the center-valued von Neumann dimension of this Hilbert module. For abelian groups with 2-cocycle satisfying Kleppner’s condition, we show that the center-valued von Neumann dimension reduces to the scalar value dπ vol(G/Γ), where dπ is the formal dimension of π and vol(G/Γ) is the covolume of Γ in G. We apply our results to characterize the existence of multiwindow super frames and Riesz sequences associated to π and Γ. In particular, we characterize when a lattice in the time-frequency plane of a second-countable, locally compact abelian group admits a Gabor frame or Gabor Riesz sequence.

• Enstad, Ulrik Bo Rufus; Jakobsen, Mads Sielemann; Luef, Franz & Omland, Tron (2022). Deformations and Balian-Low theorems for Gabor frames on the adeles. Advances in Mathematics. ISSN 0001-8708. 410. doi: 10.1016/j.aim.2022.108771. Fulltekst i vitenarkiv
• Austad, Are & Enstad, Ulrik Bo Rufus (2020). Heisenberg Modules as Function Spaces. Journal of Fourier Analysis and Applications. ISSN 1069-5869. 26(24). doi: 10.1007/s00041-020-09729-7. Fulltekst i vitenarkiv Vis sammendrag

  Let \Delta be a closed, cocompact subgroup of G \times \widehat{G}, where G is a second countable, locally compact abelian group. Using localization of Hilbert C^*-modules, we show that the Heisenberg module \mathcal {E}_{\Delta }(G) over the twisted group C^*-algebra C^*(\Delta ,c) due to Rieffel can be continuously and densely embedded into the Hilbert space L^2(G). This allows us to characterize a finite set of generators for \mathcal {E}_{\Delta }(G) as exactly the generators of multi-window (continuous) Gabor frames over \Delta , a result which was previously known only for a dense subspace of \mathcal {E}_{\Delta }(G). We show that \mathcal {E}_{\Delta }(G) as a function space satisfies two properties that make it eligible for time-frequency analysis: Its elements satisfy the fundamental identity of Gabor analysis if \Delta is a lattice, and their associated frame operators corresponding to \Delta are bounded.

• Enstad, Ulrik Bo Rufus; Jakobsen, Mads Sielemann & Luef, Franz (2019). Time-frequency analysis on the adeles over the rationals. Comptes rendus. Mathematique. ISSN 1631-073X. 357(2), s. 188–199. doi: 10.1016/j.crma.2018.12.004. Fulltekst i vitenarkiv Vis sammendrag

  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 the rationals and the group . Furthermore, we detail the connection between the construction of Gabor frames on the adeles and on with the construction of certain Heisenberg modules.

• Enstad, Ulrik Bo Rufus (2019). The Balian-Low theorem for locally compact abelian groups and vector bundles. Journal des Mathématiques Pures et Appliquées. ISSN 0021-7824. doi: 10.1016/j.matpur.2019.12.005. Fulltekst i vitenarkiv

Se alle arbeider i NVA

• Enstad, Ulrik Bo Rufus (2024). Duality principles for frames and Riesz sequences via Morita equivalence. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2024). Classifiability of C*-algebras associated with point sets. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2024). Coherent systems. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2023). Density theorems for coherent systems via point set groupoids. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2023). A dynamical approach to density theorems for sampling in unimodular groups. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2023). Spanning properties of lattice orbits of discrete series representations. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2023). Linear independence of Gabor (and other coherent) systems over discrete subgroups. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2023). Complete Gabor (and other coherent) systems over approximate lattices. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2023). Linear independence of coherent systems over lattices. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2022). Reproducing properties of lattice orbits of nilpotent Lie groups. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2022). Irregular sampling via groupoids associated to Delone sets. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2022). On sufficient conditions for lattice orbits of relative discrete series. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2022). Gabor frames over approximate lattices. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2022). Sufficient density conditions for coherent systems arising from discrete series representations. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2022). A dynamical approach to sampling and interpolation in unimodular groups. Fulltekst i vitenarkiv
• Enstad, Ulrik Bo Rufus (2021). Frames generated by unitary representations of nilpotent Lie groups. Fulltekst i vitenarkiv

Se alle arbeider i NVA