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Generalized Solutions of Operator Equations and Extreme Elements de D. A. Klyushin

Generalized Solutions of Operator Equations and Extreme Elements

Autor D. A. Klyushin, S. I. Lyashko, D. A. Nomirovskii, Yu. I. Petunin, Vladimir Semenov
en Limba Engleză Paperback – 28 noi 2013
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 recently obtained results in the study of the generalized solutions of operator equations and extreme elements in linear topological spaces. The presented results offer new methods of identifying these solutions and studying their properties. These new methods involve the application of a priori estimations and a general topological approach to construct generalized solutions of linear and nonlinear operator equations. The monograph is intended for mathematicians, graduate students and researchers studying functional analysis, operator theory, and the theory of optimal control.
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Specificații

ISBN-13: 9781461429647
ISBN-10: 1461429641
Pagini: 224
Ilustrații: XXII, 202 p.
Dimensiuni: 155 x 235 x 13 mm
Greutate: 0.35 kg
Ediția:2012
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Research

Cuprins

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.-

Recenzii

From the reviews:
“This monograph principally deals with a unified approach to the notion of generalized solutions for linear and nonlinear operator equations between Banach spaces X and Y and, to a smaller degree, to the notion of generalized solutions to extremal problems for real functions defined on a set M of a Banach space. … this book is written sufficiently well and is easy readable. Undoubtedly, it will be interesting for all specialists in Functional Analysis and Partial Differential Equations.” (P. P. Zabreĭko, Mathematical Reviews, Issue 2012 j)
“This is a well-written, self-contained and easily readable monograph, with a reasonable number of references to English written papers and books. It can be recommended to everyone interested in the topic and having some background in functional analysis and topology.” (Robert Plato, Zentralblatt MATH, Vol. 1240, 2012)

Textul de pe ultima copertă

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.

Caracteristici

Contains recently obtained results in linear operator theory with applications to optimal control theory Provides new methods of identifying solutions of linear and nonlinear operator equations Can serve as a text in graduate courses and seminars in functional analysis and optimal control theory Includes supplementary material: sn.pub/extras