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Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.

0 votes
1 answer
135 views

A minimal surface with a local extremum in normal direction is a plane [closed]

I'm currently struggling with concluding a proof and need a hint. So the first part of the exercise was that given an open subset $\Omega \subset \mathbb{R}^2$ and a harmonic function $f: \Omega \to \ …
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1 answer
706 views

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 $\hat{k}$ …