Memoirs of the American Mathematical Society 1995; 138 pp; softcover Volume: 113 ISBN10: 082180359X ISBN13: 9780821803592 List Price: US$43 Individual Members: US$25.80 Institutional Members: US$34.40 Order Code: MEMO/113/542
 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. Readership 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. Table of Contents  Introduction
 Regular SturmLiouville problem
 Singular SturmLiouville problem
 Polynomial solutions
 Polynomial examples
 The four representative examples
 Leftdefinite spaces
 References
