The nuclear-spaces tag has no wiki summary.

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### Measure theory in nuclear spaces

Much of the literature on measure theory in linear spaces focuses on the case of normed linear spaces (e.g., the outstanding book by Vakhania, or its sequel). However, nuclear linear spaces "as far ...

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### What functions can be obtained as a convolution of a Schwartz function and a tempered distribution?

Let $\mathcal S (\mathbb R)$ denote the space of Schwartz functions on $\mathbb R$ and $\mathcal S^* (\mathbb R)$ denote the dual space of Schwartz (a.k.a tempered) distributions.
We consider ...

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### Schwartz Kernel theorem for tempred functions

Let $T(R)$ denote the space of tempered functions on the line,
i.e. the smooth functions that give Schwartz function after a
multiplication by any Schwartz function, equipped with the natural
nuclear ...

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### Exactness of completed tensor product of nuclear spaces

Let $0 \to V \to W \to L \to 0$ be a strict short exact sequence
of (complete) nuclear spaces, i.e. it is a short exact sequence of
(complete) nuclear spaces, all the maps are continuous, the map ...

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### Hom of Nuclear spaces

Let V be a Nuclear space (not necessary Frechet, but complete). Let V^* be the dual space considered with the weak topology (i.e. pointwise convergence). Is it true that $V^*$ is also nuclear?
Is it ...

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### Is the category of smooth manifolds equivalent to the opposite category of the category of commutative monoids of some additive symmetric monoidal category?

This is a followup to my previous question, which asked whether
the category of commutative or noncommutative C*-algebras or von Neumann algebras
is equivalent to the category of commutative or ...

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### Are extensions of nuclear Fréchet spaces nuclear?

Consider the category of Fréchet spaces, the morphisms being
continuous linear maps with closed image. Suppose that we
have a short exact sequence in that category:
$0 \rightarrow V_1 \rightarrow ...