Seminars and Colloquia
Mathematics
On fractional multi-singular Schr\"odinger operators: positivity and localization of binding
Thu, Feb 14, 2019,
02:30 PM to 03:30 PM
at Madhava Hall
Dr. Debangana Mukherjee
Masaryk University, Brno, Czech Republic
In this work, we investigate the positivity properties of nonlocal
Schr\\"odinger type operators, driven by the fractional Laplacian, with multipolar critical locally homogeneous potentials. On one hand, we develop a criterion that links the positivity of the spectrum of such operators with the existence of certain positive supersolutions, while, on the other hand, we study the localization of
binding for this kind of potentials. Combining these two tools and performing an inductive procedure on the number of poles, we establish necessary and sufficient conditions for the existence of a configuration of poles that ensures the positivity of the corresponding Schr\\"odinger operator. This is joint work with Veronica Felli and Roberto Ognibene.
Schr\\"odinger type operators, driven by the fractional Laplacian, with multipolar critical locally homogeneous potentials. On one hand, we develop a criterion that links the positivity of the spectrum of such operators with the existence of certain positive supersolutions, while, on the other hand, we study the localization of
binding for this kind of potentials. Combining these two tools and performing an inductive procedure on the number of poles, we establish necessary and sufficient conditions for the existence of a configuration of poles that ensures the positivity of the corresponding Schr\\"odinger operator. This is joint work with Veronica Felli and Roberto Ognibene.
