On p.27 of this paper (https://arxiv.org/pdf/hep-ph/0409313) by John Collins, he says that when defining PDFs in terms of partonic number operators, one acquires an IR-divergent bare PDF (eq. 52). The residue of the IR-divergent term is proportional to the DGLAP splitting kernels:
Now, when we solve the DGLAP equations formally, we find the solution
Is the $f_i(x,\mu^2_0)$ the same IR-bare PDF from above? Can I see the splitting kernels as a kind of IR counter terms to cancel the remaining IR divergence in the bare PDF?