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.
Semester
This course gives a detailed introduction to the spectral theory of boundary value problems for SturmLiouville 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, WeylTitchmarsh 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. Autumn 2011 (Monday, October 10 to Friday, December 16) Timetable
Students
PrerequisitesThe course is planned to be selfcontained and only requires knowledge of
mathematical analysis. Some familiarity with ordinary differential equations
and/or linear operator theory will be helpful.
Syllabus
Bibliography
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AssignmentsSpectral theory of ordinary differential operators  course assessment
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