# Tagged Questions

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### How to integrate an exponential function of an exponential function?

Does any one know how to calculate the following integration? $$\int_{\mathbb{R}} \left(\exp(z \: e^{-y^2})-1\right)^2 dy=?,\quad z>0.$$ This post is related to my previous question here , ...
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### Generalized Radon transform with limited hyperplanes

The generalized Radon transform maps a function $f \in L^1(\mathbb R^n)$, usually interpreted as a density of an object, to its integral value over an $(n-1)$-dimensional affine subspace. To be more ...
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### Quantitative Weierstrass Approximation and Paley-Wiener for the Laplace Transform II

This is a modification of a previous question. Question: Suppose $a(s)\in C^\infty([0,1])$ and $H(s,x)\in C^\infty([0,1]\times [0,1])$ with $H(s,x)>0$, $\forall s,x\in [0,1]$. Suppose, ...
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### Complex structure on $L^2(\mathbb R)$ generalizing the Hilbert transform.

The Hilbert transform on the real Hilbert space $L^2(\mathbb R)$ is the singular integral operator $$\mathcal H(f)(x) := \frac{1}{\pi} \int_{-\infty}^\infty \frac{1}{x-y} f(y) dy.$$ It satisfies ...
### Integral kernel of form $e^{-<x,y>^2}$
Let $K(x,y): \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}$ given by $K(x,y) = e^{-< x,y>^2}$ where $<\cdot,\cdot>$ denote the canonical inner product. Define integral operator ...