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Volume 28, Issue 2
Recursive Reproducing Kernels Hilbert Spaces Using the Theory of Power Kernels

M. Mouattamid

Anal. Theory Appl., 28 (2012), pp. 111-124.

Published online: 2012-06

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  • Abstract

The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recursively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.

  • AMS Subject Headings

46E22, 46B70, 41A05, 47B34, 41D65, 65D05, 65D15

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COPYRIGHT: © Global Science Press

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@Article{ATA-28-111, author = {}, title = {Recursive Reproducing Kernels Hilbert Spaces Using the Theory of Power Kernels}, journal = {Analysis in Theory and Applications}, year = {2012}, volume = {28}, number = {2}, pages = {111--124}, abstract = {

The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recursively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.

}, issn = {1573-8175}, doi = {https://doi.org/10.3969/j.issn.1672-4070.2012.02.002}, url = {http://global-sci.org/intro/article_detail/ata/4548.html} }
TY - JOUR T1 - Recursive Reproducing Kernels Hilbert Spaces Using the Theory of Power Kernels JO - Analysis in Theory and Applications VL - 2 SP - 111 EP - 124 PY - 2012 DA - 2012/06 SN - 28 DO - http://doi.org/10.3969/j.issn.1672-4070.2012.02.002 UR - https://global-sci.org/intro/article_detail/ata/4548.html KW - Hilber space, reproducing kernel, interpolant, power function and Conditionally positive kernel. AB -

The main objective of this work is to decompose orthogonally the reproducing kernels Hilbert space using any conditionally positive definite kernels into smaller ones by introducing the theory of power kernels, and to show how to do this decomposition recursively. It may be used to split large interpolation problems into smaller ones with different kernels which are related to the original kernels. To reach this objective, we will reconstruct the reproducing kernels Hilbert space for the normalized and the extended kernels and give the recursive algorithm of this decomposition.

M. Mouattamid. (1970). Recursive Reproducing Kernels Hilbert Spaces Using the Theory of Power Kernels. Analysis in Theory and Applications. 28 (2). 111-124. doi:10.3969/j.issn.1672-4070.2012.02.002
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