content_image/331870.jpg content_image/331871.jpg content_image/331873.jpg content_image/331872.jpg
Eq. (A6) is the natural building block for the desired convolution kernel. Indeed, accord- ing to the definition of the gluon forward like functions G ( E ) 2 ν ( y, t ) with n = 2 ν + l − 1 

<img src='content_image/331870.jpg'>

Using (A7) together with (A6) it is straightforward to check that the integral convolution 

<img src='content_image/331871.jpg'>

results in the formal series (18). 

The trick that allows to derive the expression for the convolution kernel consists in the explicit calculation of the discontinuity of F (2 ν $^{)}$( z, y ) at z = x stemming from the cut at 1 − √ 1 − ξ 2 < x$_{s}$ < 1 + √ 1 − ξ 2 and from possible poles at z$_{s}$ = 0: 1 ( E ) (2 ν 

<img src='content_image/331873.jpg'>

Finally, the expression for the gluon GPD H g ( E ) through the set of the forward like functions reads 

<img src='content_image/331872.jpg'>

where the functions H g ( E ) ( ν $^{)}$( x, ξ, t ) defined for − ξ ≤ x ≤ 1 are given by the following 

