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arXiv · 2311.16747

A Note on the Completeness of All Translates of a Function in the Orlicz Spaces

Bhawna Dharra·S. Sivananthan
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Abstract

We give a characterization of those functions whose all translates are complete in certain Orlicz space $L^{\Phi}(\mathbb{R})$. As a consequence, we identified those discrete sets $\Lambda \subseteq \mathbb{R}$ such that there exists a function in $L^{\Phi}(\mathbb{R})$ whose $\Lambda$-translates are complete. We then prove the completeness of all translates of any simple step function in other Orlicz spaces.

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Bhawna Dharra, S. Sivananthan. 2023-11-28. A Note on the Completeness of All Translates of a Function in the Orlicz Spaces. https://arxiv.org/abs/2311.16747

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