Generalized solutions for linear operators with weakened a priori inequalities
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.
English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 8, pp 1175-1186.
Citation Example: Anikushyn A. V., Nomirovs'kii D. A. Generalized solutions for linear operators with weakened a priori inequalities // Ukr. Mat. Zh. - 2010. - 62, № 8. - pp. 1011–1021.