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

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Is Hessian operator self-adjoint on infinite dimensional environment?

As we know the Hessian matrix is symmetric in a finite-dimensional environment. What about the Hessian operator $D^2F$ for a functional $F:H\rightarrow \mathbb{R}$, where $H$ is a Hilbert space and $D …
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