Schauder frames of discrete translates in L^p(ℝ)

2024/02/15 by Nir Lev, Lev, Nir, Anton Tselishchev +1
Mathematics · #42A10 #42C15 #46B15 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2402.09915

openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For every p > (1 + √(5))/2 we construct a uniformly discrete real sequence \λ_n\_n=1^∞ satisfying |λ_n| = n + o(1), a function g ∈ L^p(ℝ), and continuous linear functionals \g^*_n\_n=1^∞ on L^p(ℝ), such that every f ∈ L^p(ℝ) admits a series expansion f(x) = ∑_n=1^∞ g_n^*(f) g(x-λ_n) convergent in the L^p(ℝ) norm. We moreover show that g can be chosen nonnegative.

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• Frame-type families of translates
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• Discrete Translates of an Operator in the Schatten p-Classes
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