Shell definition from window functions

[ntessore]

It will make some of our advanced features easier if we change the basic definition of shells from their boundaries to the matter weight functions.

That is, instead of having an increasing array of shell boundary redshifts (arXiv:2302-01942)

$$0 = z_0 < z_1 < z_2 < \ldots$$

we make the sequence of matter weight functions

$$W_1(z), W_2(z), W_3(z), \ldots$$

the fundamental definition of the shells. Shell boundaries would cease to have a meaning for GLASS.

We can then partition any function of redshift $f(z)$ into functions $f_i(z)$ for each shell using the partition of unity

$$f_i(z) = \frac{W_i(z) , f(z)}{\sum_j W_j(z)} ;.$$

The advantage of this approach is that it unifies everything from e.g. sampling galaxy redshifts to all future redshift distributions.

[ntessore]

A better idea is probably to separate the definition into window functions (currently tophat) that perform the discretisation of the shells, and a separate weight function on top of that (uniform, distance, volume, density, ...).