On the Inclusion Relation of Reproducing Kernel Hilbert Spaces

Details On the Inclusion Relation of Reproducing Kernel Hilbert Spaces On the Inclusion Relation of Reproducing Kernel Hilbert Spaces

2011-06-21

arxiv.org/abs/1106.4075v1

Mathematics

Functional Analysis

Scientific paper

To help understand various reproducing kernels used in applied sciences, we investigate the inclusion relation of two reproducing kernel Hilbert spaces. Characterizations in terms of feature maps of the corresponding reproducing kernels are established. A full table of inclusion relations among widely-used translation invariant kernels is given. Concrete examples for Hilbert-Schmidt kernels are presented as well. We also discuss the preservation of such a relation under various operations of reproducing kernels. Finally, we briefly discuss the special inclusion with a norm equivalence.

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