# Tagged Questions

**1**

vote

**0**answers

180 views

### An integral with Gamma functions (Part 2)

I was wondering if there is a generalization of the integral discussed here to a case like,
\begin{equation}\int \frac{d^dq}{q^{\nu_1}\vert \vec{q} \pm \vec{k}_1\vert ^{\nu_2}\vert \vec{q} \pm ...

**3**

votes

**1**answer

129 views

### Using Fourier Transform to speed up calculation of forces following an inverse square law

Suppose I have $n$ electric point charges in, say, two dimensions. Is there any algorithm (and I have a hunch that it might be related to the Fourier transform) to compute the net forces that act on ...

**10**

votes

**3**answers

1k views

### Fourier transforms of functions not in $L^2.$

This is probably something five-year-old physicists know, but here goes: Is there a standard methodology for computing Fourier transforms of things like $\log |x|$? Wolfram Alpha will happily give an ...

**0**

votes

**2**answers

535 views

### Do you know this form of an uncertainty principle?

I hope this question is focused enough - it's not about real problem I have, but to find out if anyone knows about a similar thing.
You probably know the Heisenberg uncertainty principle: For any ...

**2**

votes

**1**answer

696 views

### fourier transform on an interval?

Hello,
May I ask how to define the fourier transform of a function that is not defined on the whole real line?
For example, what is the fourier transform of $\frac{1}{\sqrt{x}}$? And what is the ...

**0**

votes

**2**answers

1k views

### fundamental solution of radial wave equation

i am trying to find resources on the derivation of the fundamental solution to the radial wave equation. any suggestions of or links to books, papers, and/or notes would be much appreciated. i have ...

**1**

vote

**3**answers

529 views

### Fourier Transforms restricted to mass shell

Hello,
I am stuck with the following (hopefully not too trivial) problem.
I want to know, if the map
$${\cal D}(\mathbb{R}^2)\to L^2(H_m,d\Omega_m)\qquad f \mapsto \hat{f}|_{H_m}$$
has dense range.
...

**5**

votes

**2**answers

2k views

### Can I relate the L1 norm of a function to its Fourier expansion?

I would like to express the integral of the absolute value of a real-valued function $f$ (over a finite interval) in terms of the Fourier coefficients of $f$. Failing that, I would like to know of any ...

**2**

votes

**2**answers

599 views

### Constraints on the Fourier transform of a constant modulus function

Considering the function $f:\mathbb{R} \to \mathbb{C}$, with $\left| f(x) \right|=1$ for all $x\in \mathbb{R}$.
Considering $g:\mathbb{R} \to \mathbb{C}$ with ...