Official Course Description
Symmetric and self-adjoint linear operators, such as Schrödinger operators, play an important role in mathematical physics. The course will give an introduction to the classical extension theory. This amounts to describing all self-adjoint extensions of a symmetric operator and studying their (spectral) properties. Note that for symmetric matrices (that are symmetric operators in a finite dimensional space) this question is void, whereas e.g. in connection with differential operators (in spaces of functions) a rich structure waits to be explored. We will illustrate the results by examples from different areas.