Analysis/PDE Reading Seminar
Fall 2019
Date: | October 15, 2019 |
Time: | 4:00pm |
Location: | BLOC624 |
Speaker: | Gregory Berkolaiko, Texas A&M University |
Title: | Self-adjoint extensions via boundary triples |
Abstract: | To better understand self-adjoint extensions of symmetric operators via boundary triples (and associated topics such as Krein resolvent formula), we will consider how this theory works for matrices. The analog of a symmetric operator is a rectangular matrix. Because its domain isn't dense, its adjoint is not a matrix but must be interpreted as a linear relation. With this understanding, the rest of the theory follows. Some interesting links emerge, for example the Dirichlet-to-Neumann map is a Schur complement in the matrix case. |
Date: | October 22, 2019 |
Time: | 4:00pm |
Location: | BLOC 624 |
Speaker: | Gregory Berkolaiko, Texas A&M University |
Title: | Self-adjoint extensions via boundary triples (part II) |
Abstract: | To better understand self-adjoint extensions of symmetric operators via boundary triples (and associated topics such as Krein resolvent formula), we will consider how this theory works for matrices. The analog of a symmetric operator is a rectangular matrix. Because its domain isn't dense, its adjoint is not a matrix but must be interpreted as a linear relation. With this understanding, the rest of the theory follows. Some interesting links emerge, for example the Dirichlet-to-Neumann map is a Schur complement in the matrix case. In the first part we reviewed the general theory. In the second we will play with the simple example of linear operators on C^3 (i.e. 3x3 matrices). |