All Questions

Let $f : \mathbb R_+ \to \mathbb C$ be a measurable and integrable function where $\mathbb R_+ = [0,\infty)$. The Laplace transform of $f$ is given by $$ Lf(s) = \int_0^\infty f(x)e^{-sx} \, dx. $$ A ...

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 ...

I am currently dealing with discrete Fourier transform and correlation technique to construct the spectrum of a broad band signal. It's already known that if I have enough observations of the signal, ...

I would like to know if the Prolate Spheroidal Wavefunctions (PSWFs, defined below) are in $L^1(\mathbb{R})$. I know that they are square integrable, but cannot decide about absolute integrability. ...

I am trying to understand the Wiener-Ikehara Tauberian theorem which can be a step to understanding the prime number theorem. Let $$ \hat{a}(s) = \int_0^\infty e^{-us}\, da(u) $$ with $a(u)$ some ...