The Gelfand–Shilov Type Estimate for Green’s Function of the Bounded Solutions Problem

Abstract

An analogue of the Gelfand-Shilov estimate of the matrix exponential is proved for Green's function of the problem of bounded solutions of the ordinary differential equation x ′ (t) − Ax(t) = f (t).1991 Mathematics Subject Classification. 47A60; 15A16; 65F60; 65D05; 34B27; 34B40; 34D09.