# Questions tagged [fa.functional-analysis]

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

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### Is the Borel lemma projection a smooth principal bundle?

Consider the Fréchet spaces $C^\infty(\mathbb{R},\mathbb{R})$ and $\mathbb{R}^\infty$, and the continuous linear map $$J\colon C^\infty(\mathbb{R},\mathbb{R}) \to \mathbb{R}^\infty$$ returning the ...
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### Criteria for tightness of Gaussian measures on Banach spaces

In Bogachev's book "Gaussian Measures" (Example 3.8.13) sufficient conditions for the (uniform) tightness of a sequence of centered Borel Gaussian probability measures on a separable Hilbert ...
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### Is $\phi(t)=\|P(w+td)-w\|_X/t$ nonincreasing if $X$ is "only" a uniformly smooth and uniformly convex reflexive Banach space?

For a Hilbert space $X$ it is known that the function $\phi(t)=\frac{1}{t}\|P(w+td)-w\|_X$ with $t>0$ is nonincreasing. Here, $P:X\to C$ denotes the projection operator and $w \in C, d \in X$ are ...
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### Explicit estimates on summability kernels

A "summability kernel" is a sequence of functions $k_n:[0,1)\to \mathbb C$ such that $$\int_0^1 k_n(t) \mathrm d t =1,$$ $$\int_0^1 |k_n(t)| \mathrm d t =O(1),$$ with an implied constant ...
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### Square-root lattices: where do they appear?

As an experimental physicist working on crystallography I'm often dealing with the reconstruction of an object from intensity data that emerge from an imaging device. In mathematics the problem is ...
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