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Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials

Available Formats:
Electronic ISBN: 978-1-4704-0121-4
Product Code: MEMO/113/542.E
List Price: $46.00 MAA Member Price:$41.40
AMS Member Price: $27.60 Click above image for expanded view Second-Order Sturm-Liouville Difference Equations and Orthogonal Polynomials Available Formats:  Electronic ISBN: 978-1-4704-0121-4 Product Code: MEMO/113/542.E  List Price:$46.00 MAA Member Price: $41.40 AMS Member Price:$27.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1131995; 138 pp
MSC: Primary 39;

This well-written 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 Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. Discussing the self-adjointness 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 second-order difference operator to be self-adjoint 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 self-adjoint when restricted to “energy norms”. This book is suitable as a text for an advanced graduate course on Sturm-Liouville operators or on applied analysis.

Specialists in Sturm-Liouville 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 Sturm-Liouville problem
• 3. Singular Sturm-Liouville problem
• 4. Polynomial solutions
• 5. Polynomial examples
• 6. The four representative examples
• 7. Left-definite spaces
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Volume: 1131995; 138 pp
MSC: Primary 39;

This well-written 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 Sturm-Liouville boundary value problems for difference equations, generalizing many of the known results for differential equations. Discussing the self-adjointness 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 second-order difference operator to be self-adjoint 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 self-adjoint when restricted to “energy norms”. This book is suitable as a text for an advanced graduate course on Sturm-Liouville operators or on applied analysis.