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

2023/11/28 by Bhawna Dharra, Dharra, Bhawna, Sivananthan, S.
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.2311.16747

Abstract

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

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