Further properties of Gaussian Reproducing Kernel Hilbert Spaces
Minh Ha Quang
TL;DR
This paper extends the understanding of Gaussian Reproducing Kernel Hilbert Spaces by developing a continuous family of orthonormal bases, enhancing theoretical insights into their structure.
Contribution
It introduces a generalized, infinite family of orthonormal bases for Gaussian RKHS, building upon previous discrete basis constructions.
Findings
Established a continuous parametrization of orthonormal bases
Generalized previous basis constructions to an infinite family
Implications for theoretical analysis of Gaussian RKHS
Abstract
We generalize the orthonormal basis for the Gaussian RKHS described in \cite{MinhGaussian2010} to an infinite, continuously parametrized, family of orthonormal bases, along with some implications. The proofs are direct generalizations of those in \cite{MinhGaussian2010}.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Numerical methods in inverse problems · Approximation Theory and Sequence Spaces