Course Catalog

MATH 604 Unbounded Operators in Hilbert Spaces 3 Credits
The course is an introduction to the theory of unbounded operators in Hilbert spaces and consists of two parts: Part 1 develops the general theory of unbounded operators. The main topics here are domains, graphs, adjoint operators, spectrum, resolvent, symmetric operators and quadratic forms, symmetric extensions, deficiency indices, self-adjoint operators, Cayley transform, Spectral theorem, Stone theorem. Part 2 is an introduction to the spectral theory of differential operators (Sturm-Liouville operators and Hill-Schrödinger operators). The main topics include domains, spectra localization, asymptotics of eigenvalues and eigenfunctions, bases of root functions, convergence of spectral decompositions.

Last Offered Terms Course Name SU Credit
Spring 2010-2011 Unbounded Operators in Hilbert Spaces 3

Prerequisite: __
Corequisite: __
ECTS Credit: 10 ECTS (10 ECTS for students admitted before 2013-14 Academic Year)
General Requirements: