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arXiv · 2312.11039

Schauder frames of discrete translates in $L^2(\mathbb{R})$

Nir Lev·Anton Tselishchev
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Abstract

We construct a uniformly discrete sequence $\{λ_1 < λ_2 < \cdots\} \subset \mathbb{R}$ and functions $g$ and $\{g_n^*\}$ in $L^2(\mathbb{R})$, such that every $f \in L^2(\mathbb{R})$ admits a series expansion \[ f(x) = \sum_{n=1}^{\infty} \langle f, g_n^* \rangle \, g(x-λ_n) \] convergent in the $L^2(\mathbb{R})$ norm.

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BibTeXRIS

Nir Lev, Anton Tselishchev. 2025-12-20. Schauder frames of discrete translates in $L^2(\mathbb{R})$. https://arxiv.org/abs/2312.11039

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