Uniformly bounded Lebesgue constants for scaled cardinal interpolation with Matérn kernels (Q2124221)

The author interpolates a data function at the points of a scaled grid from a space using series representations. Some preliminary materials on cardinal interpolation with Matérn kernels, including the Fourier representation of the corresponding Lagrange functions are presented. The main result of the paper and convergence properties are obtained. The results obtained differ in several aspects from the one in the literature and they are used to obtain a uniform bound on the Lebesgue constants for a non-stationary cardinal interpolation with the Matérn kernel. They also provide convergence results for approximation with Matérn and related compactly supported polyharmonic kernels.