Operator Functions And Operator Equations
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Linear Operator Equations: Approximation And Regularization
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be.This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Operator Functions And Operator Equations
This book is devoted to norm estimates for operator-valued functions of one and two operator arguments, as well as to their applications to spectrum perturbations of operators and to linear operator equations, i.e. to equations whose solutions are linear operators. Linear operator equations arise in both mathematical theory and engineering practice. The norm estimates suggested in the book have applications to the theories of ordinary differential, difference, functional-differential and integro-differential equations, as well as to the theories of integral operators and analytic functions. This book provides new tools for specialists in matrix theory and functional analysis. A significant part of the book covers the theory of triangular representations of operators that was developed by L de Branges, M S Brodskii, I C Gohberg, M G Krein, M S Livsic and other mathematicians.
Operator Functions and Operator Equations
"This book is devoted to norm estimates for operator-valued functions of one and two operator arguments, as well as to their applications to spectrum perturbations of operators and to linear operator equations, i.e. to equations whose solutions are linear operators. Linear operator equations arise in both mathematical theory and engineering practice. The norm estimates suggested in the book have applications to the theories of ordinary differential, difference, functional-differential and integro-differential equations, as well as to the theories of integral operators and analytic functions. This book provides new tools for specialists in matrix theory and functional analysis. A significant part of the book covers the theory of triangular representations of operators that was developed by L de Branges, M S Brodskii, I C Gohberg, M G Krein, M S Livsic and other mathematicians."--Publisher's website.