Generalized Solutions of Operator Equations and Extreme Elements - Klyushin, D.A.; Lyashko, S.I.; Nomirovskii, D.A.; Petunin, Yu.I.; Semenov, V.V.; SpringerLink (Online service) (New York, NY : Springer New York, 2012)
The abstract models for many problems in science and engineering take the form of an operator equation; the resolution of these problems often requires determining the existence and uniqueness of solutions to these equations. Generalized Solutions of Operator Equations and Extreme Elements presents a general functional analytic approach to solving operator equations in a general form. This unique and valuable monograph presents recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The results are clearly and thoroughly presented and offer new methods of identifying these solutions and studying their properties. These methods are based on a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. This volume is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control. Prerequisites include knowledge of basic functional analysis.
Preface -- 1. Fundamental notions, general and auxiliary facts -- 2. Simplest schemes of generalized solution of linear operator equations -- 3. A priori estimations for linear continuous operator -- 4. Applications of the theory of generalized solvability of linear equations -- 5. Scheme of generalized solutions of linear operator equations -- 6. Scheme of generalized solutions of nonlinear operator equations -- 7. Generalized extreme elements -- Reference.-.
Keywords: Mathematics; Functional equations; Operator theory; Mathematical optimization; Topology; Mathematics; Calculus of Variations and Optimal Control; Optimization; Operator Theory; Difference and Functional Equations; Topology