TY - JOUR
T1 - Recursive Reproducing Kernels Hilbert Spaces Using the Theory of Power Kernels
AU - M. Mouattamid
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 - <p style="text-align: justify;">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.</p>