Convergence properties of spline-like cardinal interpolation operators acting on l^p data

2013/12/14 by Jeff Ledford, Ledford, Jeff
Computer Science · Engineering · Mathematics · #41A05 #41A15 #41A30 #41A65 #Advanced Numerical Analysis Techniques #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #math.FA #msc:41A05 #msc:41A15 #msc:41A30 #msc:41A65

paper · pdf · doi:10.48550/arxiv.1312.4062

14 pages

arxiv created 2013/12/14 · openalex publication_date 2013/12/14 · arxiv updated 2013/12/17 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

If f∈ \f∈ L^p(ℝ): f(x)=∫_-π^πe^ixξdβ(ξ), β∈ B.V.([-π,π]) \, then f is determined by its samples on the integers by taking an appropriate limit. Specifically, ‖ f - L_ϕαf ‖_L^p(ℝ)→ 0 as α→∞ provided that \ϕ_α: α∈ A\ is what we call a spline-like family of cardinal interpolators.

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