# Questions tagged [fa.functional-analysis]

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

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### Bounded approximation property and affine subspaces of codimension $1$

Let $E$ be a Banach space with the bounded approximation property and let $M\subseteq E$ be an affine subset of co-dimension $1$, and let $C\subseteq M$ be a closed and convex subset of $M$ with non-...
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### Pertrubing the approximation property from the Lipschitz-free space to stay in the Wasserstein space

Let $(X,d,x)$ be a separable pointed metric space and let $\mathcal{F}(X)$ be its Arens-Eells (also called its Lipschitz-Free space; in the case where $X$ is Banach) space. We view the $1$-...
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### Knowledge on weighted integral operators?

There are tons of books and a huge literature on the properties of the following integral operator: \begin{equation} T(f) = \int_{\mathcal{X}} K(x,\cdot)f(x)dx, \end{equation} where $K(x,z)$ is, say, ...
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### product of two generalized functions

Let $f_n$ and $g_n$ two generalized functions such that : the product $f_n g_n$ is well defined for all $n\in \mathbb{N}$, which means $WF(f_n)+WF(g_n)$ does not contain an element of the form $(x,0)$...
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### Differential properties of the Radon transform

I am looking for a reference for the following fact: Let $f \in L_1(\mathbb{R}^{d})$ that has compact support and that is also in $C^{s}(\mathbb{R}^{d})$. We define the Radon transform of $f$ as: \...
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### Compact embedding of Lipschitz continuous functions

Let $(X,d,\mu)$ be a metric measure space, not necessarily with $\mu(X)<\infty$. I would like to study the embedding of $W^{1,2}(X)\cap \mathrm{Lip}(X)$ into $L^2(X)$. Are there simple conditions ...
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### Pointwise convergence of kernels of Hilbert-Schmidt operators

Lately I was discussing different types of convergence for Hilbert-Schmidt operators and during that discussion we ended up talking about pointwise convergence of Fourier series. I have already asked ...
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### Taylor coefficients of Hadamard product

I imagine this to be a very classical question in complex analysis: Consider the Hadamard product $$g(\mu) = \prod_{n=1}^{\infty}E_1(\mu z_n),$$ where $E_1(z):=(1-z)e^z$ is the first elementary ...
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### The symmetric group of positive integers acting on $\ell^\infty(\mathbb{N})^*$

Let $\mathfrak{S}_\mathbb{N}$ be the symmetric group of all positive integers. Let $\ell^\infty(\mathbb{N})^*$ be the dual space of $\ell^\infty(\mathbb{N})$ equipped with weak*-topology. There is a ...
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### (Sharp) Bounds on $E(XYZ)$ given all the bivariate marginals

Suppose $X,Y,Z$ are all real-valued random variables. Suppose I know the joint marginal distributions of $(X,Y)$, $(Y,Z)$ and $(X,Z)$. I want to find bounds on $E(XYZ)$. In the case of bounding $E(XY)$...
Suppose that $\Omega=[0,1]^2$. I will say that a real valued function $u$ on $\Omega$ satisfies periodic boundary values if $$u(x,0)=u(x,1), \;u(0,y)=u(1,y),\;\;\;\text{ for all }x,y\in[0,1].$$ Now ...