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This graduate textbook offers an introduction to the spectral
theory of ordinary differential equations, focusing on
Sturm-Liouville equations.Sturm-Liouville theory has applications
in partial differential equations and mathematical physics.
Examples include classical PDEs such as the heat and wave
equations. Written by leading experts, this book provides a modern,
systematic treatment of the theory. The main topics are the
spectral theory and eigenfunction expansions for Sturm-Liouville
equations, as well as scattering theory and inverse spectral
theory. It is the first book offering a complete account of the
left-definite theory for Sturm-Liouville equations. The modest
prerequisites for this book are basic one-variable real analysis,
linear algebra, as well as an introductory course in complex
analysis. More advanced background required in some parts of the
book is completely covered in the appendices. With exercises in
each chapter, the book is suitable for advanced undergraduate and
graduate courses, either as an introduction to spectral theory in
Hilbert space, or to the spectral theory of ordinary differential
equations. Advanced topics such as the left-definite theory and the
Camassa-Holm equation, as well as bibliographical notes, make the
book a valuable reference for experts.
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