Spectral Theory of Partial Differential Equations - Lecture Notes

Details Spectral Theory of Partial Differential Equations - Lecture Notes Spectral Theory of Partial Differential Equations - Lecture Notes

2012-03-11

arxiv.org/abs/1203.2344v1

Mathematics

Analysis of PDEs

120 pages; 37 figures

Scientific paper

This mini-course of 20 lectures aims at highlights of spectral theory for self-adjoint partial differential operators, with a heavy emphasis on problems with discrete spectrum. Part I: Discrete Spectrum (ODE preview, Laplacian - computable spectra, Schroedinger - computable spectra, Discrete spectral theorem via sesquilinear forms, Laplace eigenfunctions, Natural boundary conditions, Magnetic Laplacian, Schroedinger in confining well, Variational characterizations, Monotonicity of eigenvalues, Weyl's asymptotic, Polya's conjecture, Reaction-diffusion stability, Thin fluid film stability) Part II: Continuous Spectrum (Laplacian on whole space, Schroedinger with $-2sech^2$ potential, Selfadjoint operators, Spectra: discrete and continuous, Discrete spectrum revisited)

Affiliated with

Also associated with

No associations

Rating

Spectral Theory of Partial Differential Equations - Lecture Notes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Spectral Theory of Partial Differential Equations - Lecture Notes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Spectral Theory of Partial Differential Equations - Lecture Notes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-14623