# A graduate course on Sturm Liouville theory?

Dear Math community,

               I have some general questions on Sturm-Liouville theory. We are planning to introduce a graduate course on Sturm-Liouville theory and every one has been asked to propose topics which might be suitable for the course.


I would like to know the following.

1. Is it worth to have a course exclusively on just Sturm-Liouville theory?

2. If we have a course like that what are the topics that could be introduced in the course?

3. Would it be possible for an exclusive course on sturm-liouville theory without much background in functional analysis.

Any suggestions would be really appreciated.

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A more advanced/comprehensive course can be based on Atkinson's book Discrete and continuous boundary problems. No functional analysis is required, neither for Hilbert-Courant nor for Atkinson. (When Courant wrote the first volume of HC, functional analysis did not exist yet:-)

Another book which studies some of these questions in depth (and without any functional analysis) is Gantmakher-Krein, Oscillation matrices and kernels. (Gantmaher, Gantmacher...)

Is it worth offering such a course? The answer depends on whether you can find enough students who will enroll. This depends on your local conditions. Of course this is a beautiful and useful subject and worth learning.

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Thanks for your comments and suggestions. I do have one more question. I think the students who might be taking this course are more oriented toward algebra. Is it possible to have a little bit of an algebraic flavor to this course? –  user8974 Apr 12 '13 at 3:00
Yes, and Atkinson's book is good for this. It has more algebraic flavor on my opinion, because he considers discrete and continuous problems together. Same applies to Krein-Gantmakher book. –  Alexandre Eremenko Apr 12 '13 at 12:38