Zobrazeno 1 - 10
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pro vyhledávání: '"Oussa, Vignon"'
Autor:
Oussa, Vignon
The HRT (Heil-Ramanathan-Topiwala) posits the linear independence of any set of nonzero square-integrable vectors obtained from a single nonzero vector $f$ by applying a finite set of time-frequency shift operators. In this short note, we present fin
Externí odkaz:
http://arxiv.org/abs/2305.12299
Autor:
Führ, Hartmut, Oussa, Vignon
We study the phase retrieval property for orbits of general irreducible representations of nilpotent groups, for the classes of simply connected connected Lie groups, and for finite groups. We prove by induction that in the Lie group case, all irredu
Externí odkaz:
http://arxiv.org/abs/2201.08654
Autor:
Okoudjou, Kasso A., Oussa, Vignon
The HRT (Heil-Ramanathan-Topiwala) conjecture stipulates that the set of any finitely many time-frequency shifts of a non-zero square Lebesgue integrable function is linearly independent. The present work settles two special cases of this conjecture,
Externí odkaz:
http://arxiv.org/abs/2110.04053
We study phase retrieval for group frames arising from permutation representations, focusing on the action of the affine group of a finite field. We investigate various versions of the phase retrieval problem, including conjugate phase retrieval, sig
Externí odkaz:
http://arxiv.org/abs/2109.07123
In this paper, we study the spectrality and frame-spectrality of exponential systems of the type $E(\Lambda,\varphi) = \{e^{2\pi i \lambda\cdot\varphi(x)}: \lambda\in\Lambda\}$ where the phase function $\varphi$ is a Borel measurable which is not nec
Externí odkaz:
http://arxiv.org/abs/2007.03736
Publikováno v:
In Linear Algebra and Its Applications 15 November 2023 677:161-193
We present a new infinite family of full spark frames in finite dimensions arising from a unitary group representation, where the underlying group is the semi-direct product of a cyclic group by a group of automorphisms. The only previously known alg
Externí odkaz:
http://arxiv.org/abs/1909.06223
Autor:
Oussa, Vignon
Let $G=NH$ be a Lie group where $N,H$ are closed connected subgroups of $G,$ and $N$ is an exponential solvable Lie group which is normal in $G.$ Suppose furthermore that $N$ admits a unitary character $\chi_{\lambda}$ corresponding to a linear funct
Externí odkaz:
http://arxiv.org/abs/1811.10468
Autor:
Currey, Brad, Oussa, Vignon
We prove that the HRT (Heil, Ramanathan, and Topiwala) conjecture is equivalent to the conjecture that finite translates of square-integrable functions on the Heisenberg group are linearly independent.
Comment: 11 pages
Comment: 11 pages
Externí odkaz:
http://arxiv.org/abs/1811.10463
Autor:
Fuhr, Hartmut, Oussa, Vignon
Let $G$ be a locally compact group with left regular representation $\lambda_{G}.$ We say that $G$ admits a frame of translates if there exist a countable set $\Gamma\subset G$ and $\varphi\in L^{2}(G)$ such that $(\lambda_{G}(x) \varphi)_{x \in\Gamm
Externí odkaz:
http://arxiv.org/abs/1802.02658