Completeness of uniformly discrete translates in LP(ℝ)

Nir Lev

doi:10.1007/s11854-025-0361-8

Completeness of uniformly discrete translates in L^P(ℝ)

Nir Lev

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We construct a real sequence {λ_n}_n=1^∞ satisfying λ_n = n + o(1), and a Schwartz function f on ℝ, such that for any N the system of translates {f(x − λ_n)}, n > N, is complete in the space L^p(ℝ) for every p > 1. The same system is also complete in a wider class of Banach function spaces on ℝ.

Original language	English
Journal	Journal d'Analyse Mathematique
DOIs	https://doi.org/10.1007/s11854-025-0361-8
State	Accepted/In press - 2025

All Science Journal Classification (ASJC) codes

Analysis
General Mathematics

Access to Document

10.1007/s11854-025-0361-8

Cite this

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title = "Completeness of uniformly discrete translates in LP(ℝ)",

abstract = "We construct a real sequence {λn}n=1∞ satisfying λn = n + o(1), and a Schwartz function f on ℝ, such that for any N the system of translates {f(x − λn)}, n > N, is complete in the space Lp(ℝ) for every p > 1. The same system is also complete in a wider class of Banach function spaces on ℝ.",

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AB - We construct a real sequence {λn}n=1∞ satisfying λn = n + o(1), and a Schwartz function f on ℝ, such that for any N the system of translates {f(x − λn)}, n > N, is complete in the space Lp(ℝ) for every p > 1. The same system is also complete in a wider class of Banach function spaces on ℝ.

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JF - Journal d'Analyse Mathematique