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I have several related questions on Analytic functions and Hyperfunction as topological vector spaces (I am mainly interested in questions 4,6,10): For an open set $U\subset \mathbb C^n$ we can ...

I am looking for a short introduction to nuclear spaces and nuclear operators. I am interested in these spaces as they often arise in mathematically rigorous quantum field theories. I have read the ...

Recently, I'd come across the following kind of operators and I wonder if they have been considered before and given a name. Let's say that a linear map $T:V\to W$ between locally convex topological ...

Let $\substack{\text{lim} \\ \leftarrow i} H_i$ be a nuclear space, considered as the limit of the codirected diagram $$... \to H_2 \to H_1 \to H_0,$$ with $f_{ji}:H_i \to H_j$ being the trace class ...

Denote by $\mathscr{D}^\prime$ and $\mathscr{D}^\prime_b$ the space of distributions on $\mathbb{R}^n$ equipped with the weak and the strong topology, respectively. Because the topology of $\mathscr{D}...

In a short biography article on Alexander Grothendieck, it is mentioned that after Grothendieck submitted his first thesis on topological vector spaces (TVS), apparently, he told Bernard Malgrange ...