
10/15 4:00pm 
BLOC624 
Gregory Berkolaiko Texas A&M University 
Selfadjoint extensions via boundary triples
To better understand selfadjoint 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 DirichlettoNeumann map is a Schur complement in the matrix case. 

10/22 4:00pm 
BLOC 624 
Gregory Berkolaiko Texas A&M University 
Selfadjoint extensions via boundary triples (part II)
To better understand selfadjoint 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 DirichlettoNeumann 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). 