Entire solutions of one linear implicit differential-difference equation in Banach spaces - Gefter, S. L.; Piven’, A. L. (Ukrains’kyi Matematychnyi Zhurnal, 2018)
We establish the existence and uniqueness conditions for the solution for the initial problem Bu′ (z) = Au(z + h) + f(z), z C, u(0) = u_0 in the classes of entire functions of exponential type. Closed linear operators A and B act on Banach spaces and can be degenerate. We also present an example of application of abstract results to partial differential equations.