arXiv subjects
Publications and source records attributed to Bhawna Dharra.
In this manuscript, we investigate the properties of systems formed by translations of an operator in the Schatten $p$-classes $\mathcal{T}^p$. We establish the existence of Schauder frames of integer translates in $\mathcal{T}^p$ for $p>2$. Later, we provide an instance of a uniformly discrete $Λ\subset \mathbb{R}^{2d}$ such that there exists an operator whose $Λ$-translates are complete in $\mathcal{T}^p$ for all $p>1$.
We give a characterization of those functions whose all translates are complete in certain Orlicz space $L^Φ(\mathbb{R})$. As a consequence, we identified those discrete sets $Λ\subseteq \mathbb{R}$ such that there exists a function in $L^Φ(\mathbb{R})$ whose $Λ$-translates are complete. We then prove the completeness of all translates of any simple step function in other Orlicz spaces.
We provide a characterization of discrete sets $Λ\subset \mathbb{R}$ that admit a function whose $Λ$-translates are complete in the Hardy space $H^1(\mathbb{R})$. In particular, we show that such a set cannot be uniformly discrete. We then give a uniformly discrete $Λ\subset \mathbb{R}$ which admits a pair of functions such that their $Λ$-translates are complete in $H^1(\mathbb{R})$.