# A general sampling theory in the functional Hilbert space induced by a Hilbert space valued kernel

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Let â„ be a separable Hilbert space and Î© fixed subset of â„. Consider an â„ valued function K : Î© â†’ â„ and x Ïµ â„ . Then, the function fx : Î© â†’ â„‚ given by fx (t) := âŸ¨x,K(t)âŸ©â„ is well-defined. Denote by HK the set of...

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