On the Inclusion Relation of Reproducing Kernel Hilbert Spaces

@article{Zhang2011OnTI,
  title={On the Inclusion Relation of Reproducing Kernel Hilbert Spaces},
  author={Haizhang Zhang and Liang Zhao},
  journal={ArXiv},
  year={2011},
  volume={abs/1106.4075}
}
  • Haizhang Zhang, Liang Zhao
  • Published in ArXiv 2011
  • Mathematics, Computer Science
  • 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… CONTINUE READING

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    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 26 REFERENCES

    Refinement of Reproducing Kernels

    VIEW 5 EXCERPTS

    Scattered Data Approximation

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Theory of Reproducing Kernels.

    VIEW 10 EXCERPTS
    HIGHLY INFLUENTIAL

    Frames

    • H. Zhang, J. Zhang
    • Riesz bases, and sampling expansions in Banach spaces via semi-inner products, Appl. Comput. Harmon. Anal. 31
    • 2011
    VIEW 1 EXCERPT

    Refinable Kernels

    VIEW 3 EXCERPTS

    Multiscale kernels

    VIEW 2 EXCERPTS