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arXiv · 2208.03748

Fourier analysis in spaces of shifts

A. Yu. Ulitskaya
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Abstract

In this paper, we develop a continual analog of decomposition over orthogonal bases in spaces generated by equidistant shifts of a single function. By doing so, we obtain an explicit expression for best approximation by spaces of shifts in $L_2(\mathbb{R})$. The result is formulated in terms of classical Fourier transform and tends to have various applications in approximation by spaces of shifts and, in particular, in spline approximation.

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A. Yu. Ulitskaya. 2022-08-07. Fourier analysis in spaces of shifts. https://arxiv.org/abs/2208.03748

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