Functional analysis is the study of infinite-dimensional vector spaces, often with additional structures (inner product, norm, topology), with typical examples given by function spaces. The subject also includes the study of linear and non-linear operators on these spaces, as well as measure, ...

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When is the Laplace Beltrami Operator self-adjoint?

The Laplace-Beltrami operator is an operator which is the typical example of a self-adjoint operator in $L^{2}$. I am wondering if this is also true for other Hilbert spaces $W^{k,2}$. If this is ...
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Hölder continuous functions are of 1st category in $C[0,1]$

I'm trying to show that the Hölder continuous functions in $[0,1]$ are a set of first category in $C[0,1]$. Does it suffice to show that they are not an open subset of $C[0,1]$? Let ...
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Why has the Stein operator for normal approximations the form $(\mathcal Af)(x)=f^\prime(x)-xf(x)$?

My Question: Why has the Stein operator $\mathcal A$ for normal approximations the form $(\mathcal Af)(x)=f^\prime(x)-xf(x)$? How can one deduce this form of the operator? Reason for my question: I ...