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Almost homogeneous Schroedinger operators

Jan Derezinski
(Warsaw University)
Math/Phys Seminar
Wednesday, 15 February, 2017, at 15:15-16:15, in Aud. D1 (1531-113)
Abstract:
First I will describe a certain natural holomorphic family of closed operators  with interesting spectral properties. These operators  can be fully analyzed using just trigonometric functions. 

Then I will discuss 1-dimensional Schroedinger operators with a 1/x^2 potential with general boundary conditions, which I studied recently with S.Richard. Even though their description involves Bessel and Gamma functions, they turn out to be equivalent to the previous family.

Some  operators that I will describe are  homogeneous--they get multiplied by a constant after a change of the scale. In general, their homogeneity is weakly broken--scaling induces a simple but nontrivial flow in the parameter space. One can say (with some exaggeration) that they can be viewed as "toy models of the renormalization group".

Contact person: Erik Skibsted