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

Abstract

If $f\in \{f\in L^p(\mathbb{R}):f(x)={\int }_{-\pi }^{\pi }{e}^{ix\xi }d\beta (\xi ),\beta \in B.V.([-\pi ,\pi ])\}$, then $f$ is determined by its samples on the integers by taking an appropriate limit. Specifically, $\Vert f-L_{{\varphi }_{\alpha }}f{\Vert }_{L^p(\mathbb{R})}\to 0$ as $\alpha \to \infty$ provided that $\{{\varphi }_{\alpha }:\alpha \in A\}$ is what we call a spline-like family of cardinal interpolators.

14 pages

References in corpus (1)

• On the Convergence of Regular Families of Cardinal Interpolators

Cited by in corpus (3)

• Cardinal Interpolation With General Multiquadrics
• Regular Families of Kernels for Nonlinear Approximation
• On regular families of cardinal interpolators and multiresolution analyses