Electronic ISBN:  9781470401214 
Product Code:  MEMO/113/542.E 
List Price:  $46.00 
MAA Member Price:  $41.40 
AMS Member Price:  $27.60 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 113; 1995; 138 ppMSC: Primary 39;
This wellwritten book is a timely and significant contribution to the understanding of difference equations. Presenting machinery for analyzing many discrete physical situations, the book will be of interest to physicists and engineers as well as mathematicians. The book develops a theory for regular and singular SturmLiouville boundary value problems for difference equations, generalizing many of the known results for differential equations. Discussing the selfadjointness of these problems as well as their abstract spectral resolution in the appropriate \(L^2\) setting, the book gives necessary and sufficient conditions for a secondorder difference operator to be selfadjoint and have orthogonal polynomials as eigenfunctions. These polynomials are classified into four categories, each of which is given a properties survey and a representative example. Finally, the book shows that the various difference operators defined for these problems are still selfadjoint when restricted to “energy norms”. This book is suitable as a text for an advanced graduate course on SturmLiouville operators or on applied analysis.
ReadershipSpecialists in SturmLiouville operators, differential equations and difference equations, as well as those in other areas who wish to apply the results to other cases.

Table of Contents

Chapters

1. Introduction

2. Regular SturmLiouville problem

3. Singular SturmLiouville problem

4. Polynomial solutions

5. Polynomial examples

6. The four representative examples

7. Leftdefinite spaces


Request Review Copy

Get Permissions
 Book Details
 Table of Contents

 Request Review Copy
 Get Permissions
This wellwritten book is a timely and significant contribution to the understanding of difference equations. Presenting machinery for analyzing many discrete physical situations, the book will be of interest to physicists and engineers as well as mathematicians. The book develops a theory for regular and singular SturmLiouville boundary value problems for difference equations, generalizing many of the known results for differential equations. Discussing the selfadjointness of these problems as well as their abstract spectral resolution in the appropriate \(L^2\) setting, the book gives necessary and sufficient conditions for a secondorder difference operator to be selfadjoint and have orthogonal polynomials as eigenfunctions. These polynomials are classified into four categories, each of which is given a properties survey and a representative example. Finally, the book shows that the various difference operators defined for these problems are still selfadjoint when restricted to “energy norms”. This book is suitable as a text for an advanced graduate course on SturmLiouville operators or on applied analysis.
Specialists in SturmLiouville operators, differential equations and difference equations, as well as those in other areas who wish to apply the results to other cases.

Chapters

1. Introduction

2. Regular SturmLiouville problem

3. Singular SturmLiouville problem

4. Polynomial solutions

5. Polynomial examples

6. The four representative examples

7. Leftdefinite spaces