On the Laplacian perturbed with inverse square potential: the domain of its closure and of its square – Mario Rastrelli (Università di Pisa)


Aula Seminari


Abstract: Perturbation of operators is a very rich branch of the modern analysis. The perturbation of Laplacian with inverse square potential arises, in particular, in the studies of non linear Schrödinger equation. So, in this talk, we want to give an explicit and easy characterization of the domain of the operator $A_\beta=-\Delta+\frac{\beta}{|x|^2}$. Such characterization is also usefull to determine the domain of $A_\beta^2$ in a similar way. The study of these operators gives to us a new proof of weighted perturbed Rellich inequalities.

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