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Relations Between Reproducing Kernel Hilbert Spaces

In: Detection of Random Signals in Dependent Gaussian Noise

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  • Antonio F. Gualtierotti

    (University of Lausanne, HEC and IDHEAP)

Abstract

When one claims that the signal must be in the RKHS of the noise, for detection to be nonsingular, one in fact means that the family of its paths should be contained, as a set, in the RKHS of that noise. One shall see in the next chapter that such a requirement entails a specific inclusion of related RKHS’s, and the entire topic may be seen as a partial answer to the following question: given an RKHS of signals, which noises does it accommodate? What follows covers thus relations between RKHS’s and, in particular inclusions and intersections.

Suggested Citation

  • Antonio F. Gualtierotti, 2015. "Relations Between Reproducing Kernel Hilbert Spaces," Springer Books, in: Detection of Random Signals in Dependent Gaussian Noise, chapter 0, pages 217-305, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-22315-5_3
    DOI: 10.1007/978-3-319-22315-5_3
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