Hilbert Spaces Induced by Toeplitz Covariance Kernels
نویسندگان
چکیده
We consider the reproducing kernel Hilbert space Hμ induced by a kernel which is obtained using the Fourier-Stieltjes transform of a regular, positive, finite Borel measure μ on a locally compact abelian topological group Γ. Denote by G the dual of Γ. We determine Hμ as a certain subspace of the space C0(G) of all continuous function on G vanishing at infinity. Our main application is calculating the reproducing kernel Hilbert spaces induced by the Toeplitz covariance kernels of some well-known stochastic processes. AMS Subj. Class. Primary: 60B15, Secondary: 60G10, 46C15.
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