(x , x - x ') + \frac{x - \zeta}{x - x'}
\Theta_{11}^0 (x - \zeta, x - x ') \right]_+
+ \frac{1}{2} \delta (x ' - x) \right\},\end{aligned}$$ where $\Theta^0_{11} (x, x') = (\theta(x) - \theta(x'))/(x - x')$. The corresponding ER-BL kernel ($\zeta=1$) $$\begin{aligned}
V^T ( x, x' ) \equiv - K^T (x , x', 1)
= C_F
\left\{
\left[
\theta( x' - x ) \frac{x}{x'} \frac{1}{x' - x}
+ \theta(x - x') \frac{\bar x}{\bar x'}\frac{1}{x - x'} \right]_+
+ \frac{1}{2} \delta (x - x')\right\},\end{aligned}$$ and the DGLAP kernel ($\zeta=0$ and $z=x/x'$) $$\begin{aligned}
P^T (z) \equiv - K^T (z x' , x', 0)
= C_F
\left\{
2 \left[ \frac{z}{\bar z} \right]_+
+
\frac{1}{2} \delta (\bar z)
\right\}\end{aligned}$$ follow immediately from the generalized one (\[gen-ker-KT\]).

In order to find the solution of the evolution equations of the type given in Eq. (\[MOMEE\]) we are looking for the conformal spin expansion in terms of reduced non-forward expectation values of conformal twist-2 operators which are related to the Gegenbauer moments of the corresponding distributions, namely, for quark function we have $$\begin{aligned}
\zeta^j
\int dx C_j^\frac{3}{2}\left( 2\frac{x}{\zeta} - 1 \right)
{^Q\!{\cal O}^{\mit\Gamma}} (x, \zeta) =
\langle h'| {^Q\!{\cal O}}^{\mit\Gamma}_{jj} |h \rangle .\end{aligned}$$ $C^\nu_j$ 