Harald Woracek (TU Wien)
Colloquium of the Department of Mathematics and Computer Science
Thursday January 23 17:15 room 105 (14-th line V.I., 29)
We discuss a topic which occurs in the spectral theory of two-dimensional canonical systems. A canonical system is a differential equation of the form, where the Hamiltonian H is a positive semidefinite-matrix valued function on the half-line normalised by a.e.
By H.Weyl’s nested disks method a function , mapping the upper half-plane analytically into itself, can be constructed. This function, called the Weyl coefficient, plays an important role: it allows to construct a scalar spectral measure for the differential operator induced by the equation.
It is a common meta-principle that the high-energy behaviour of , i.e., its behaviour towards, is related to the behaviour of the corresponding Hamiltonian towards 0. In this talk we instantiate this principle by means of several theorems giving explicit connections towards and locally at 0.
Everyone is welcome!