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<p>We construct a real sequence {<i>λ</i><sub><i>n</i></sub>}<Stack> <sub><i>n</i>=1</sub> <sup>∞</sup> </Stack> satisfying <i>λ</i><sub><i>n</i></sub> = <i>n</i> + <i>o</i>(1), and a Schwartz function <i>f</i> on ℝ, such that for any <i>N</i> the system of translates {<i>f</i>(<i>x</i> − <i>λ</i><sub><i>n</i></sub>)}, <i>n</i> &gt; <i>N</i>, is complete in the space <i>L</i><sup><i>p</i></sup>(ℝ) for every <i>p</i> &gt; 1. The same system is also complete in a wider class of Banach function spaces on ℝ.</p>

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Completeness of uniformly discrete translates in LP(ℝ)

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  • 发表日期：

    2025年1月21日

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  • Nir Lev

摘要

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.