I must prepare a seminar about spectral theory of linear partial differential operators. However, I'm at a loss as to a nice reference. I'm looking for something that fits in a graduate spectral theory course.
My teacher was following the book Introductory Functional Analysis (I. Kreyszig) (which is not too advanced) so the exposition must be at the same level (but if needed I have the freedom to use Fourier analysis and Sobolev Spaces).
Furtheremore, I should deal with the spectrum of the Laplacian operator.
Books and class notes recommendations are both welcome.
Thanks.