# Tagged Questions

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

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### Various limits of the Christoffel Darboux Kernel

In a different thread, we stumbled upon the following question: Given a continuous finite measure $w(x)dx$ on some interval $(a,b)$, $-\infty \leq a <b \leq \infty$, and the set of respective ...
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### intuitive connection between The KdV equations and the Virasoro bott group

I posted this on stack exchange but had no joy, perhaps someone here can answer : The Euler Arnold equation expresses equations (usually from mathematical physics) as geodesic equations on a Lie group....
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### Attempted Banachification of a space

In a recent blog post, Terry Tao mentioned the question of how to tell if a Hausdorff topological vector space admits a finer topological structure which happens to be the topology of a Banach space (...
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### Functions $f \in S(\mathbb{R})$ with slow decay rate?

I came across this question by thinking about whether there are functions $f \in S(\mathbb{R})$ that satisfy for all(!) $a>0$ that $f e^{a|.|^a} \notin L^{\infty},$ as somebody on math....
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### A continuous functional calculus on/positive elements in a Fréchet algebra?

I am trying to understand what (minimal) conditions one would need in order to obtain a functional calculus on a Fréchet algebra, which we demand to be equipped with an involution that leaves all semi-...
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### Can we say translation/dilation of the $L^p-$multiplier is again a $L^{p}-$multiplier?

Suppose that $m:\mathbb R \to \mathbb C$ such that $\| (m \hat{f})^{\vee} \|_{L^{p}} \leq C \|f\|_{L^{p}}$ (where $C$ is some constant, $f\in L^{p}$). (That is, $m$ is an $L^{p}-$ multiplier) ...
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### Multilinear Interpolation

Suppose I have a multilinear map $\Gamma(u,v)$ satisfying \begin{align} \big\| \Gamma(u,v)\big\|_{L^2} &\leq \big\| u\big\|_{L^2} \big\| v\big\|_{L^2} \\ \big\| \Gamma(u,v)\big\|_{L^\infty} &\...