# Tag Info

1 vote
Accepted

### Convolution And deconvolution of functions

All this text is just verbalizing that the pdf of the sum of two independent random variates is the convolution of their respective pdf-s. That is if you have two rv-s, say $\mathbf {x,y}$ and their ...
• 19.3k
1 vote
Accepted

### Resolution and delta function

A 'delta function' is actually a distribution (a generalized function) that only can be computed in combination with an integration-over-a-range. The delta distribution is an ideal one to represent a ...
• 9,883

### Does the exponential representation of Dirac delta function depend on choice of Fourier convention?

The equation you wrote is a mathematical statement and as such it should not (and it doesn't) depend on any convention. Its proper meaning is intended in the sense of distribution. The distribution on ...
• 2,384

### Does the exponential representation of Dirac delta function depend on choice of Fourier convention?

The identity $$\delta(\omega) = \frac{1}{2\pi} \int dt\, e^{i\omega t}$$ does not depend on the Fourier convention (but of course requires regularization of the integral). When you use a different ...
• 11.8k
1 vote

### Closed form expression of 2D CFT integral

A very common integral which is almost enough to prove this is \int \frac{d^2 z}{|z - w_1|^{2\beta_1} |z - w_2|^{2\beta_2}} = \frac{\Gamma(\beta_1 + \beta_2 - 1)}{\Gamma(2 - \beta_1 - ...
• 7,790