Polynomial Operator Equations in Abstract Spaces and Applications

Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is more likely due to the fact that polynomial operators - unlike polynomials in a single variable - have received little attention. Consequently, this comprehensive presentation is needed, benefiting those working in the field as well as those seeking information about specific results or techniques.
Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings.
Topics include:

  • Special cases of nonlinear operator equations
  • Solution of polynomial operator equations of positive integer degree n
  • Results on global existence theorems not related with contractions
  • Galois theory
  • Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas
  • Results on the various Chandrasekhar equations
  • Weierstrass theorem
  • Matrix representations
  • Lagrange and Hermite interpolation
  • Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space
    The materials discussed can be used for the following studies
  • Advanced numerical analysis
  • Numerical functional analysis
  • Functional analysis
  • Approximation theory
  • Integral and differential equation
  • 1101427155
    Polynomial Operator Equations in Abstract Spaces and Applications

    Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is more likely due to the fact that polynomial operators - unlike polynomials in a single variable - have received little attention. Consequently, this comprehensive presentation is needed, benefiting those working in the field as well as those seeking information about specific results or techniques.
    Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings.
    Topics include:

  • Special cases of nonlinear operator equations
  • Solution of polynomial operator equations of positive integer degree n
  • Results on global existence theorems not related with contractions
  • Galois theory
  • Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas
  • Results on the various Chandrasekhar equations
  • Weierstrass theorem
  • Matrix representations
  • Lagrange and Hermite interpolation
  • Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space
    The materials discussed can be used for the following studies
  • Advanced numerical analysis
  • Numerical functional analysis
  • Functional analysis
  • Approximation theory
  • Integral and differential equation
  • 82.99 In Stock
    Polynomial Operator Equations in Abstract Spaces and Applications

    Polynomial Operator Equations in Abstract Spaces and Applications

    by Ioannis K. Argyros
    Polynomial Operator Equations in Abstract Spaces and Applications

    Polynomial Operator Equations in Abstract Spaces and Applications

    by Ioannis K. Argyros

    eBook

    $82.99 

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    Overview

    Polynomial operators are a natural generalization of linear operators. Equations in such operators are the linear space analog of ordinary polynomials in one or several variables over the fields of real or complex numbers. Such equations encompass a broad spectrum of applied problems including all linear equations. Often the polynomial nature of many nonlinear problems goes unrecognized by researchers. This is more likely due to the fact that polynomial operators - unlike polynomials in a single variable - have received little attention. Consequently, this comprehensive presentation is needed, benefiting those working in the field as well as those seeking information about specific results or techniques.
    Polynomial Operator Equations in Abstract Spaces and Applications - an outgrowth of fifteen years of the author's research work - presents new and traditional results about polynomial equations as well as analyzes current iterative methods for their numerical solution in various general space settings.
    Topics include:

  • Special cases of nonlinear operator equations
  • Solution of polynomial operator equations of positive integer degree n
  • Results on global existence theorems not related with contractions
  • Galois theory
  • Polynomial integral and polynomial differential equations appearing in radiative transfer, heat transfer, neutron transport, electromechanical networks, elasticity, and other areas
  • Results on the various Chandrasekhar equations
  • Weierstrass theorem
  • Matrix representations
  • Lagrange and Hermite interpolation
  • Bounds of polynomial equations in Banach space, Banach algebra, and Hilbert space
    The materials discussed can be used for the following studies
  • Advanced numerical analysis
  • Numerical functional analysis
  • Functional analysis
  • Approximation theory
  • Integral and differential equation

  • Product Details

    ISBN-13: 9781000142457
    Publisher: CRC Press
    Publication date: 10/07/2020
    Sold by: Barnes & Noble
    Format: eBook
    Pages: 586
    File size: 20 MB
    Note: This product may take a few minutes to download.

    About the Author

    Argyros, Ioannis K.

    Table of Contents

    Introduction 1. Quadratic Equations and Perturbation Theory 2. More Methods for Solving Quadratic Equations 3. Polynomial Equations in Banach Space 4. Integral and Differential Equations 5. Polynomial Operators in Linear Spaces 6. General Methods for Solving Nonlinear Equations
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