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Softcover ISBN:  9780821852675 
Product Code:  SURV/121.S 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413484 
Product Code:  SURV/121.S.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821852675 
eBook ISBN:  9781470413484 
Product Code:  SURV/121.S.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 121; 2005; 328 ppMSC: Primary 34; Secondary 47
In 1836 and 1837, Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which began the subject now known as the Sturm–Liouville theory. In 1910, Hermann Weyl published an article which started the study of singular Sturm–Liouville problems. Since then, Sturm–Liouville theory has remained an intensely active field of research with many applications in mathematics and mathematical physics.
The purpose of the present book is (a) to provide a modern survey of some of the basic properties of SturmLiouville theory and (b) to bring the reader to the forefront of research on some aspects of this theory. Prerequisites for using the book are a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory. The book has an extensive list of references and examples and numerous open problems. Examples include classical equations and functions associated with Bessel, Fourier, Heun, Ince, Jacobi, Jörgens, Latzko, Legendre, LittlewoodMcLeod, Mathieu, Meissner, and Morse; also included are examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.
This book offers a wellorganized viewpoint on some basic features of Sturm–Liouville theory. With many useful examples treated in detail, it will make a fine independent study text and is suitable for graduate students and researchers interested in differential equations.
ReadershipGraduate students and research mathematicians interested in differential equations.

Table of Contents

Chapters

1. First order systems

2. Scalar initial value problems

3. Twopoint regular boundary value problems

4. Regular selfadjoint problems

5. Regular leftdefinite and indefinite problems

6. Oscillation

7. The limitpoint, limitcircle dichotomy

8. Singular initial value problems

9. Twopoint singular boundary value problems

10. Singular selfadjoint problems

11. Singular indefinite problems

12. Singular leftdefinite problems

13. Two intervals

14. Examples

15. Notation

16. Comments on some topics not covered

17. Open problems


Additional Material

Reviews

In summary, this monograph offers a wealth of information on SturmLiouville theory and is an ideal textbook for a course in this field, serves as an indispensible source for every researcher working in this area, is ideally suited for selfstudy due to its detailed proofs and comprehensive bibliography, and is recommended to any applied scientist who wants to use SturmLiouville theory.
Zentralblatt MATH 
...this monograph is a valuable and important work, useful for all people interested in the theory of secondorder linear differential operators.
Mathematical Reviews


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In 1836 and 1837, Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which began the subject now known as the Sturm–Liouville theory. In 1910, Hermann Weyl published an article which started the study of singular Sturm–Liouville problems. Since then, Sturm–Liouville theory has remained an intensely active field of research with many applications in mathematics and mathematical physics.
The purpose of the present book is (a) to provide a modern survey of some of the basic properties of SturmLiouville theory and (b) to bring the reader to the forefront of research on some aspects of this theory. Prerequisites for using the book are a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory. The book has an extensive list of references and examples and numerous open problems. Examples include classical equations and functions associated with Bessel, Fourier, Heun, Ince, Jacobi, Jörgens, Latzko, Legendre, LittlewoodMcLeod, Mathieu, Meissner, and Morse; also included are examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.
This book offers a wellorganized viewpoint on some basic features of Sturm–Liouville theory. With many useful examples treated in detail, it will make a fine independent study text and is suitable for graduate students and researchers interested in differential equations.
Graduate students and research mathematicians interested in differential equations.

Chapters

1. First order systems

2. Scalar initial value problems

3. Twopoint regular boundary value problems

4. Regular selfadjoint problems

5. Regular leftdefinite and indefinite problems

6. Oscillation

7. The limitpoint, limitcircle dichotomy

8. Singular initial value problems

9. Twopoint singular boundary value problems

10. Singular selfadjoint problems

11. Singular indefinite problems

12. Singular leftdefinite problems

13. Two intervals

14. Examples

15. Notation

16. Comments on some topics not covered

17. Open problems

In summary, this monograph offers a wealth of information on SturmLiouville theory and is an ideal textbook for a course in this field, serves as an indispensible source for every researcher working in this area, is ideally suited for selfstudy due to its detailed proofs and comprehensive bibliography, and is recommended to any applied scientist who wants to use SturmLiouville theory.
Zentralblatt MATH 
...this monograph is a valuable and important work, useful for all people interested in the theory of secondorder linear differential operators.
Mathematical Reviews