Multivariate Interpolation Using Linear Combinations of Translates of a Conditionally Positive Definite Function
In this paper, we discuss “cardinal” as well as “infinite scattered data” interpolation using finite linear combination of translates of a conditionally positive definite function. We prove that for a subclass of such functions, the cardinal interpolation operators are bounded and invertible on lp, 1 ≤ p≤ I ∞.In some special cases, including “Hardy's multiquadrics” and “The Thin Plate Spline,” we show that the scattered data interpolation operators are bounded and invertible on l2.
Guo, K., S. Hu, and Xingping Sun. "Multivariate interpolation using linear combinations of translates of a conditionally positive definite function." Numerical functional analysis and optimization 14, no. 3-4 (1993): 371-381.
Numerical Functional Analysis and Optimization