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A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.

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Norm of derivative of rank one projector

I asked this question on math.stack but I got no answer, so I try here. Let $\phi(t)$ be a solution for the nonlinear Schroedinger equation\begin{equation} i\partial_t\phi(t)=-\Delta\phi(t)+(V*|\phi| …
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