Conditionally Positive Definite Functions and Laplace-Stieltjes Integrals
نویسندگان
چکیده
منابع مشابه
Pointwise Estimates Formultivariate Interpolation Using Conditionally Positive Definite Functions
We seek pointwise error estimates for interpolants, on scattered data, constructed using a basis of conditionally positive deenite functions of order m, and polynomials of degree not exceeding m-1. Two diierent approaches to the analysis of such interpolation are considered. The former uses distributions and reproducing kernel ideas, whilst the latter is based on a Lagrange function approach. E...
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In this paper, we consider a broad class of interpolation problems, for both scalarand vector-valued multivariate functions subject to linear side conditions, such as being divergence-free, where the data are generated via integration against compactly supported distributions. We show that, by using certain families of matrix-valued conditionally positive definite functions, such interpolation ...
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Conditionally positive definite kernels provide a powerful tool for scattered data approximation. Many nice properties of such methods follow from an underlying reproducing kernel structure. While the connection between positive definite kernels and reproducing kernel Hilbert spaces is well understood, the analog relation between conditionally positive definite kernels and reproducing kernel Po...
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For a certain constant δ > 0 (a little less than 1/4), every function f : N0 → ]0,∞[ satisfying f(n)2 ≤ δf(n − 1)f(n + 1), n ∈ N, is a Stieltjes indeterminate Stieltjes moment sequence. For every indeterminate moment sequence f : N0 → R there is a positive definite matrix sequence (an) which is not of positive type and which satisfies tr(an+2) = f(n), n ∈ N0. For a certain constant ε > 0 (a lit...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 1993
ISSN: 0021-9045
DOI: 10.1006/jath.1993.1065