Mercer’s Theorem on General Domains: On the Interaction between Measures, Kernels, and RKHSs

@article{Steinwart2012MercersTO,
  title={Mercer’s Theorem on General Domains: On the Interaction between Measures, Kernels, and RKHSs},
  author={Ingo Steinwart and C. Scovel},
  journal={Constructive Approximation},
  year={2012},
  volume={35},
  pages={363-417}
}
Given a compact metric space X and a strictly positive Borel measure ν on X, Mercer’s classical theorem states that the spectral decomposition of a positive self-adjoint integral operator Tk:L2(ν)→L2(ν) of a continuous k yields a series representation of k in terms of the eigenvalues and -functions of Tk. An immediate consequence of this representation is that k is a (reproducing) kernel and that its reproducing kernel Hilbert space can also be described by these eigenvalues and -functions. It… Expand
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