Almost homogeneous Schroedinger operator

Mercredi 15 novembre 16:00-17:00 - Jan Dereziński - Warsaw university

Résumé : 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 ».
Based on
J.D. Laurent Bruneau and Vladimir Georgescu : Homogeneous Schrödinger operators on half-line, Annales Henri Poincare 12 (2011), 547-590
J.D., Serge Richard : On Schrödinger operators with inverse square potentials on the half-line, Annales Henri Poincare 18 (2017) 869-928
J.D. : Homogeneous rank one perturbations, to appear in Annales Henri Poincare

Lieu : salle 228, bâtiment 440

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