Operator Functions and Operator Equations

Nonfiction, Science & Nature, Mathematics, Matrices, Functional Analysis
Cover of the book Operator Functions and Operator Equations by Michael I Gil', World Scientific Publishing Company
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Michael I Gil' ISBN: 9789813221284
Publisher: World Scientific Publishing Company Publication: September 8, 2017
Imprint: WSPC Language: English
Author: Michael I Gil'
ISBN: 9789813221284
Publisher: World Scientific Publishing Company
Publication: September 8, 2017
Imprint: WSPC
Language: English

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.

Contents:

  • Preliminaries
  • Representations of Solutions to Operator Equations
  • Functions of Finite Matrices
  • Solution Estimates for Polynomial Matrix Equations
  • Two-sided Matrix Sylvester Equations
  • Bounds for Condition Numbers of Diagonalizable Matrices
  • Functions of a Compact Operator in a Hilbert Space
  • Triangular Representations of Non-selfadjoint Operators
  • Resolvents of Bounded Non-selfadjoint Operators
  • Regular Functions of a Bounded Non-selfadjoint Operator
  • Functions of an Unbounded Operator
  • Similarity Condition Numbers of Unbounded Diagonalizable Operators
  • Commutators and Perturbations of Operator Functions
  • Functions of Two Non-commuting Operators in Hilbert Spaces

Readership: Undergraduate and graduate students, and researchers in matrix theory, functional analysis and their applications to differential and difference equations.
Key Features:

  • Presents norm estimates for functions of two operator arguments and their applications
  • Gives a systematic exposition of solution estimates of linear operator equations
  • Suggests bounds for the similarity condition numbers of diagonalizable operators
  • The published results concerning the functions of one operator argument in this book are considerably simplified and supplemented
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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.

Contents:

Readership: Undergraduate and graduate students, and researchers in matrix theory, functional analysis and their applications to differential and difference equations.
Key Features:

More books from World Scientific Publishing Company

Cover of the book 2014 Regional Competitiveness Analysis and a Master Plan on Regional Development Strategies for India by Michael I Gil'
Cover of the book Advances in Cooperative Robotics by Michael I Gil'
Cover of the book The Story of Genetics, Development and Evolution by Michael I Gil'
Cover of the book Tan Kah-Kee by Michael I Gil'
Cover of the book Pioneers of Medicine Without a Nobel Prize by Michael I Gil'
Cover of the book Neuroprosthetics by Michael I Gil'
Cover of the book European Economic Integration, WTO Membership, Immigration and Offshoring by Michael I Gil'
Cover of the book Matrices by Michael I Gil'
Cover of the book Studies in Foreign Exchange Economics by Michael I Gil'
Cover of the book The Strong Nonlinear Limit-Point/Limit-Circle Problem by Michael I Gil'
Cover of the book Elements of Human Voice by Michael I Gil'
Cover of the book A Friendly Approach to Functional Analysis by Michael I Gil'
Cover of the book Aridity Trend in Northern China by Michael I Gil'
Cover of the book Cures vs. Profits by Michael I Gil'
Cover of the book Legitimacy by Michael I Gil'
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy