Generalized solutions for linear operators with weakened a priori inequalities - Anikushyn, A. V.; Nomirovs'kii, D. A. (Ukrains’kyi Matematychnyi Zhurnal, 2010)
We propose an approach to the investigation of generalized solutions of linear operators that satisfy weakened a priori inequalities. This approach generalizes several well-known definitions of generalized solutions of operator equations. We prove existence and uniqueness theorems for a generalized solution.