On Bornological Spaces of Series in Systems of Functions - Sheremeta, Myroslav (Sarajevo Journal of Mathematics, 2025)
Let f be an entire transcendental function, M_f(r) = {| f(z)| : |z| = r}, (λ_n) be a sequence of positive numbers increasing to +∞ and suppose that the series \[ A(z) = _n=1^∞ a_n f(λ_n z) \] regularly converges in C, i.e., \[ _n=1^∞ |a_n| M_f(rλ_n) < +∞ for all r [0,+∞). \] Bornology is introduced on a set of such series as a system of functions f(λ_n z), and its connection with Fréchet spaces is studied.