V. Oussa

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20122020

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math.RT2019

Full Spark Frames in the Orbit of a Representation

Romanos Diogenes Malikiosis, Vignon Oussa

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 c…

math.RT2018

Compactly supported bounded frames on Lie groups

Vignon Oussa

Let $G = N H$ 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 $N$ admit…

math.RT2018

HRT Conjecture and Linear Independence of Translates on the Heisenberg Group

Brad Currey, Vignon Oussa

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…

math.RT2018

Groups with frames of translates

Hartmut Fuhr, Vignon Oussa

Let $G$ be a locally compact group with left regular representation $λ_{G} .$ We say that $G$ admits a frame of translates if there exist a countable set $Γ \subset G$ and $φ\in L^{2…

math.RT2012

Admissibility For Quasiregular Representations of Exponential Solvable Lie Groups

Vignon Oussa

Let $N$ be a simply connected, connected non-commutative nilpotent Lie group with Lie algebra $n$ of dimension $n .$ Let $H$ be a subgroup of the automorphism group of $N…

math.RT2012

Linear Independence of a Finite Set of Dilations by a One-Parameter Matrix Lie Group

David Ferrone, Vignon Oussa

Let $G = {e^{t A} : t \in R}$ be a closed one-parameter subgroup of the general linear group of matrices of order $n$ acting on $R^{n}$ by matrix-vector multiplication…