# Descriptors¶

descriptors are simple objects that describe a function of frequencies and permits to compute it with its high frequencies expansion.

They can be combined into simple expressions. Example:

## Reference¶

class triqs.gf.descriptors.Omega

The function $$\omega \rightarrow \omega$$. If used with Matsubara Green’s functions, the corresponding class member is called iOmega_n.

class triqs.gf.descriptors.Function(function)[source]

Stores a python function

If the Green’s function is defined on an array of points $$x_i$$, then it will be initialized to $$F(x_i)$$.

class triqs.gf.descriptors.SemiCircular(half_bandwidth, chem_potential=0.0)[source]

Hilbert transform of a semicircular density of states, i.e.

$g(z) = \int \frac{A(\omega)}{z-\omega} d\omega$

where $$A(\omega) = \theta( D - |\omega|) 2 \sqrt{ D^2 - \omega^2}/(\pi D^2)$$.

(Only works in combination with frequency Green’s functions.)

class triqs.gf.descriptors.Flat(half_bandwidth)[source]

The Hilbert transform of a flat density of states, with cut-off

$g(z) = \int \frac{A(\omega)}{z-\omega} d\omega$

where $$A(\omega) = \theta( D^2 - \omega^2)/(2D)$$.

(Only works in combination with frequency Green’s functions.)