Fractional powers and singular perturbations of quantum differential Hamiltonians
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Date
2018-01
Journal Title
Journal ISSN
Volume Title
Publisher
SISSA
Abstract
We consider the fractional powers of singular (point-like) perturbations of the Laplacian and the singular perturbations of fractional powers of the Laplacian, and we compare two such constructions focusing on their perturbative structure for resolvents and on the local singularity structure of their domains. In application to the linear and non-linear Schrödinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.
Description
Dedicated to Gianfausto Dell'Antonio on the occasion of his 85th birthday
Keywords
Fractional Laplacian, Singular perturbations of differential operators, Krein-Vĭšik-Birman self-adjoint extension theory