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Can somebody give me an institution of Kernel function and why we define it in Hilbert Space and what does it means that Kernel function maps from one Hilbert space to another Hilbert space ?

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Could you please add some context and clarification of the question? What do you mean by "institution"? What do you mean by "Kernel function"? Are you referring to something related to reproducting kernel Hilbert spaces? –  Jonas Meyer Dec 4 '12 at 3:40
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