Generalized Vandermonde operator and bounded solutions of differential equations - Horodnii, M. (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.929.2We study the problem of  existence of a unique bounded solution to a linear differential equation of any order  with bounded operator coefficients. We consider the case  where the corresponding ``algebraic'' operator equation has multiple separated pairwise commuting roots. By using the generalized Vandermonde operator constructed with the help of these roots, we obtain a representation of the unique bounded solution.