On Entire Solutions of Exponential Type for Some Implicit Linear Differential-Difference Equation in a Banach Space

Abstract

Let A be a closed linear operator on a Banach space E with a possibly nondense domain. Entire solutions of exponential type of the linear differential-difference equation w′(z) = Aw(z−h)+f(z) are studied. Assuming that A has a bounded inverse, the well-posedness of this equation in a special space of entire E-valued functions is proved. Bibliography: 12 titles.