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

2024/01/28 by Lev, Nir
#42A65 #46E30 #46E50 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2401.15588

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.

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