Matrix transformations of generalized holomorphic Dirichlet series in a bounded \(\rho\)-convex domain (Q1592684)

Let \(G\) be a bounded \(\rho\)-convex domain, \(0\in G\), \((\lambda_k)^\infty_{k=1}\) be a sequence of complex numbers in \(\mathbb{C}\), \(0<|\lambda_k|\to +\infty\) as \(k\to\infty\). It is considered a generalized Dirichlet series of type \[ \sum^\infty_{k=1}c_kE_\rho(\lambda_kz),\quad z\in G, \] where \(c_k\in\mathbb{C}\) and \(E_\varrho(z)\) is the Mittag-Leffler function. The author studies the matrix transformations of such Dirichlet series.