Minimal absolutely representing systems of exponentials for A−∞(Ω)A−∞(Ω)

We study a minimal property of absolutely representing systems of exponentials EΛ=(eλkz)EΛ=(eλkz) in the space A−∞(Ω)A−∞(Ω) of holomorphic functions in a bounded convex domain ΩΩ of the complex plane CC, with polynomial growth near the boundary. A relationship between the absolutely representing property and absolutely nontrivial expansions of zero in A−∞(Ω)A−∞(Ω) is also investigated.