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Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.

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Proof: If a reproducing kernel exists for a Hilbert space, then it is unique

I really want to prove the statement in the title but I'm struggling with it. Here my current state: Proof via contradiction. Let $\mathcal{H}$ be a RKHS with two reproducing kernels $k$ and $\hat{k}$ …
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