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Open Math Notes

Resources and inspiration for math instruction and learning

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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
  • Refereed publications at the AMS

Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


Konstantin Pankrashkin
Carl von Ossietzky University of Oldenburg
MR ID: 652529
Reference #


Posted date
2020-09-08 10:23:02
Revised date
2020-09-08 10:23:02
Notes type
   Standard Course Offering
   Topics Course
      Functional Analysis
      Geometric Analysis
   Differential Equations
      Linear Partial Differential Equations
   Mathematical Physics
      Quantum Physics and Field Theory

Spectral theory and asymptotic methods

Lecture notes with some exercises. Topics include: unbounded (differential) operators, sesquilinear forms, classification of spectra, perturbations, min-max principle for eigenvalues. Schrödinger operators and Laplacians in open sets are considered as main examples. More advanced topics include decay estimates for eigenfunctions (Agmon-type estimates), semiclassical asymptotics for potential wells, Laplacians in some unbounded domains (incl. waveguides).

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v1 PDF (2.0M) 09/08/20