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Recursive Kernels

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Analysis in Theory and Applications

Abstract

This paper is an extension of earlier papers [8, 9] on the “native” Hilbert spaces of functions on some domain Ω ⊂ Rd in which conditionally positive definite kernels are reproducing kernels. Here, the focus is on subspaces of native spaces which are induced via subsets of Ω, and we shall derive a recursive subspace structure of these, leading to recursively defined reproducing kernels. As an application, we get a recursive Neville-Aitken-type interpolation process and a recursively defined orthogonal basis for interpolation by translates of kernels.

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Authors and Affiliations

  1. University of Alberta, B-01C, Campus Saint-Jean 8406, 91 Strect, Edmonton, Alberta, Tbc 4G9, Canada

    Mohammed Mouattamid

  2. Institut für Numerische und Angewandte Mathematik, Universität Göttingen, LotzestraBe 16-18, D-37083, Göttingen, Germany

    Robert Schaback

Authors
  1. Mohammed Mouattamid
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  2. Robert Schaback
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Correspondence to Mohammed Mouattamid.

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Mouattamid, M., Schaback, R. Recursive Kernels. Anal. Theory Appl. 25, 301–316 (2009). https://doi.org/10.1007/s10496-009-0301-y

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  • DOI: https://doi.org/10.1007/s10496-009-0301-y

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