Implicit linear difference equation in Frechet spaces - Gefter, S.L.; Piven, A.L. (Reports of the National Academy of Sciences of Ukraine, 2017)
An criterion of the existence and the uniqueness for a solution of the implicit linear difference equation Axn+1+Bxn=gn, where A and B are continuous operators, which act on Frechet spaces, is proved. Explicit formulas for the solution of this equation are found. For the case of Banach spaces, the results are specified