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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 ...

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 ...

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}...