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.
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