2022/08/07 by A. Yu. Ulitskaya, Ulitskaya, A. Yu.
Engineering · #41A30 #42A38 #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2208.03748
openalex publication_date 2022/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 L2(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.