Let \(L\) be an entire function of exponential type and completely regular growth with conjugate diagram \(\overline G+K\), where \(G\) is a bounded convex domain and \(K\) is a convex compact set. It is known that there exist pairwise disjoint discs \((S_j)_{j\in\mathbb N}\) of linear density zero such that \(L^{-1}(0)\cap S_j\neq\emptyset\), \(L^{-1}(0)\subset\bigcup_{j\in\mathbb N}S_j\), and \(\log|L(z)|=H_G(z)+H_K(z)+ o(|z|)\) as \(z\longrightarrow\infty\), \(z\notin\bigcup_{j\in\mathbb N}S_j\) (\(H_G\) and \(H_K\) denote the support functions). Let \(E_j\) be the vector subspace (of the space \(A(G)\) of all holomorphic functions on \(G\)) spanned by the functions \(z^p\exp(\lambda z)\), \(0\leq p<\) the order of zero of \(L\) at \(\lambda\in L^{-1}(0)\cap S_j\). Take a sequence \((G_n)_{n\in\mathbb N}\) of convex compact subsets of \(G\) such that \(G_n\subset\text{int}G_{n+1}\) and \(G=\bigcup_{n\in\mathbb N}G_n\). Define \(\ell_1(\mathbb E):=\{F=(f_j)_{j\in\mathbb N}\: f_j\in E_j, \sum_{j\in\mathbb N} \sup_{G_n}|f_j|<+\infty, n\in\mathbb N\}\). The author studies the representation operator \(R:\ell_1(\mathbb E)\longrightarrow A(G)\), \(R(F):=\sum_{j\in\mathbb N}f_j\).