• Corpus ID: 53974086

On reproducing kernels, and analysis of measures

  title={On reproducing kernels, and analysis of measures},
  author={Palle E. T. Jorgensen and Feng Tian},
  journal={arXiv: Functional Analysis},
Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure: Every positive definite kernel is also the covariance kernel of a Gaussian process. Given a fixed sigma-finite measure $\mu$, we consider positive definite kernels defined on the subset of the sigma algebra having finite $\mu$ measure. We show that then the… 
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