Spectral Theory of Ordinary Differential Operators (MAGIC057) |
GeneralDescription
Ordinary differential operators appear naturally in many problems of mathematical physics
as well as questions of pure mathematics such as the stability of minimal surfaces.
Their spectra often have direct significance, e.g. as sets of vibration frequencies or admissible
energies in quantum mechanics. Moreover, ordinary differential operators provide important
and sometimes surprising examples in the spectral theory of linear operators.
This course gives a detailed introduction to the spectral theory of boundary value problems for Sturm-Liouville and related ordinary differential operators. The subject is characterised by a combination of methods from linear operator theory, ordinary differential equations and asymptotic analysis. The topics covered include regular boundary value problems, Weyl-Titchmarsh theory of singular boundary value problems, the spectral representation theorem as well as recent developments of oscillation theory as a modern tool of spectral analysis. SemesterAutumn 2011 (Monday, October 10 to Friday, December 16) Timetable
PrerequisitesThe course is planned to be self-contained and only requires knowledge of
mathematical analysis. Some familiarity with ordinary differential equations
and/or linear operator theory will be helpful.
Syllabus
Students
Bibliography
Note: Clicking on the link for a book will take you to the relevant Google Book Search page. You may be able to preview the book there. On the right hand side you will see links to places where you can buy the book. There is also link marked 'Find this book in a library'. This sometimes works well, but not always. (You will need to enter your location, but it will be saved after you do that for the first time.) AssessmentThere is a single assignment to pass the course. See under Ässignments" and follow the instructions there.
Spectral theory of ordinary differential operators - course assessment
FilesFiles marked L are intended to be displayed on the main screen during lectures.
Recorded LecturesPlease log in to view lecture recordings. |