Article
Licensed
Unlicensed
Requires Authentication
Universality of multivariate interpolation
-
Lars-Benjamin Maier
Published/Copyright:
December 10, 2013
Abstract
The aim of this article is to generalize the theory of functions “universal” with respect to interpolation operators from the univariate case introduced by Vogt [6,7] to the multivariate situation. Therefore, new arguments and different function spaces beyond mere polynomials are investigated to obtain functions f which have the following property: If one interpolates them in a certain sequence of nodal sets under certain conditions, the sequence of interpolating functions or some multiples of them allows uniform (or even stricter) approximation of any continuous function, or from a certain substantial subset of those, by a suitable subsequence.
Received: 2013-4-29
Published Online: 2013-12-10
Published in Print: 2013-12-1
© 2013 by Walter de Gruyter Berlin Boston
You are currently not able to access this content.
You are currently not able to access this content.
Articles in the same Issue
- Masthead
- Masthead
- The Cardon and Robert Criterion for the Riemann hypothesis
- Multiplications and convolutions in L. Schwartz' spaces of test functions and distributions and their continuity
- Delay difference equations: Coexistence of oscillatory and nonoscillatory solutions
- On an integral formula for differential forms and its applications on manifolds with boundary
- Some Hermite–Hadamard type inequalities for log-h-convex functions
- Asymptotic of some integral
- Argument properties of symmetric analytic functions
- Three new sequences converging to the Euler–Mascheroni constant
- Universality of multivariate interpolation
Keywords for this article
Radial basis functions;
multivariate polynomials;
interpolation;
universality
Articles in the same Issue
- Masthead
- Masthead
- The Cardon and Robert Criterion for the Riemann hypothesis
- Multiplications and convolutions in L. Schwartz' spaces of test functions and distributions and their continuity
- Delay difference equations: Coexistence of oscillatory and nonoscillatory solutions
- On an integral formula for differential forms and its applications on manifolds with boundary
- Some Hermite–Hadamard type inequalities for log-h-convex functions
- Asymptotic of some integral
- Argument properties of symmetric analytic functions
- Three new sequences converging to the Euler–Mascheroni constant
- Universality of multivariate interpolation
