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Polynomial Operator Equations in Abstract Spaces and Applications by Ioannis K. Argyros at Abbey's Bookshop,
Polynomial Operator Equations in Abstract Spaces and Applications
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Ioannis K. Argyros

Polynomial Operator Equations in Abstract Spaces and Applications

Ioannis K. Argyros

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English
CRC Press
30 June 2020
Mathematics
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
By:  
Imprint:   CRC Press
Country of Publication:   United Kingdom
Dimensions:   Height: 234mm,  Width: 156mm, 
Weight:   453g
ISBN:   9780367447878
ISBN 10:   0367447878
Pages:   586
Publication Date:  
Audience:   Professional and scholarly ,  Undergraduate
Format:   Paperback
Publisher's Status:   Active
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

Argyros, Ioannis K.

Reviews for Polynomial Operator Equations in Abstract Spaces and Applications

This book provides a valuable service to those mathematicians working in the area of polynomial operator equations...The theoretical material addressed has a spectrum of applications...applications [that are] quite relevant and important...Anyone doing research in this area should have a copy of this monograph. Patrick J. Van Fleet, Mathematical and Information Sciences, Huntsville, Texas A comprehensive presentation of this rapidly growing field...benefiting not only those working in the field but also those interested in, and in need of, information about specific results or techniques...Clear...Logical...Elegant...The author has achieved the optimum at this point. - Dr. George Anastassiou, University of Memphis, Tennessee


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