{
  "id": "1203.2344",
  "version": "v1",
  "published": "2012-03-11T15:53:38.000Z",
  "updated": "2012-03-11T15:53:38.000Z",
  "title": "Spectral Theory of Partial Differential Equations - Lecture Notes",
  "authors": [
    "Richard S. Laugesen"
  ],
  "comment": "120 pages; 37 figures",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "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)",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-11T15:53:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partial differential equations",
      "spectral theory",
      "lecture notes",
      "discrete spectrum",
      "self-adjoint partial differential operators"
    ],
    "tags": [
      "lecture notes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 120,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.2344L"
    }
  }
}