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 Using (A7) together with (A6) it is straightforward to check that the integral convolution results in the formal series (18). Finally, the expression for the gluon GPD H g ( E ) through the set of the forward like functions reads where the functions H g ( E ) ( ν $^{)}$( x, ξ, t ) defined for − ξ ≤ x ≤ 1 are given by the following 30 B g ( E ) n n +1 − 2 $_{ν}$( t ) = ∫ 1 0 dyy $^{n}$G ( E ) 2 ν ( y, t ) with n ≥ 2 ν − 1 , odd . (A7) ∞ ∑ ν =0 ∫ 1 0 dy 1 2 { disc$_{z}$$_{=}$$_{x}$ F (2 ν $^{)}$( z, y $^{) +disc$_{z}$$_{=}$}$− $_{x}$F (2 ν $^{)}$( z, y ) } G ( E ) 2 ν ( y, t ) (A8) H g ( E $^{)}$( x, ξ, t ) = ∞ ∑ ν =0 ∫ 1 0 dy 1 2 { disc$_{z}$$_{=}$$_{x}$ F (2 ν $^{)}$( z, y $^{) +disc$_{z}$$_{=}$}$− $_{x}$F (2 ν $^{)}$( z, y ) } G ( E ) 2 ν ( y, t ) = ∞ ∑ ν =0 ξ 2 ν 2 [ H g ( E ) ( ν $^{)}$( x, ξ, t ) + H g ( E ) ( ν $^{)}$( − x, ξ, t ) ] + ∞ ν =1 θ ( 1 − x 2 ξ 2 ) ( 1 − x 2 ξ 2 ) 2 ξC$^{5}$ 2 ν − 2 ( x ξ ) B g ( E ) 2 ν − $_{1 0}$( t ) , (A10) ∫ 1 0 dy G ( E ) 2 ν ( y, t ) disc$_{z}$$_{=}$$_{x}$ F (2 ν $^{)}$( z, y ) = ξ 2 ν π ∫ 1 0 dy G ( E ) 2 ν ( y, t ) ( 1 + y ∂ ∂y + 1 6 y 2 ∂ 2 ∂y 2 ) ∫ 1 − 1 ds x 2 − 2 ν s (1 − s $^{2}$) √ 2 x$_{s}$ − x 2 s − ξ 2 θ (2 x$_{s}$ − x 2 s − ξ $^{2}$) − θ ( 1 − x 2 ξ 2 ) ( 1 − x 2 ξ 2 ) 2 2 ν − 3 ∑ l =0 C$^{5}$ 2 2 ν − l − 3 ( x ξ ) ξP$_{l}$ ( 1 ξ ) ∫ 1 0 dyy 2 ν − l − $^{2}$G ( E ) 2 ν ( y, t ) . (A9) 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