All Questions

In one line: Given an exponentially decaying sine wave $x(t)$, how can we predict the amplitude of the resulting peak in frequency spectrum using discrete Fourier transform. In nuclear magnetic ...

Physicists Some people like to define the "Fourier transform" on Minkowski space as $\hat f(\xi) = \int e^{i \eta(x,\xi)} f(x) dx$, where $\eta(x,\xi)$ is the Minkowski form. I'm used to thinking of ...

I have a simple Fourier transform problem, originating from mathematical physics (system of linear PDEs), which reduces to taking the integral $$ I(\alpha)\equiv\int_{-\infty}^\infty e^{ikr} \cfrac{\...

Consider on $\mathbb{R}^{n+1}$ the indefinite quadratic form defining the Minkowski metric $$B(p)=(p^0)^2-(p^1)^2-\dots-(p^n)^2.$$ Let $\mu$ be a generalized function on $\mathbb{R}^{n+1}$ which is ...

Is there an explicit formula for the Fourier transform of the generalized function of 2 variables $$\frac{1}{x+y^2+i0}?$$ Remark. Equivalent question: consider the Schroedinger equation one the ...