INTEGRAL CAUCHY TYPE REPRESENTATIONS OF INFINITE ORDER DIFFERENTIAL OPERATORS IN SPACES OF EXPONENTIAL TYPE ENTIRE FUNCTIONS BOUNDED ON THE REAL AXIS

摘要

We obtain an integral Cauchy type representation of a vector differential operator of infinite order in the space of entire functions of exponential type that are bounded on the real axis. This representation is used for obtaining integral representations of entire solutions to explicit and implicit linear inhomogeneous differential equations in a Banach space. Bibliography: 5 titles.