@article {doi:10.1063/1.5033856,
	title = {Fractional powers and singular perturbations of quantum differential Hamiltonians},
	journal = {Journal of Mathematical Physics},
	volume = {59},
	number = {7},
	year = {2018},
	pages = {072106},
	abstract = {<p>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 Schr{\"o}dinger equations for the corresponding operators, we outline a programme of relevant questions that deserve being investigated.</p>},
	doi = {10.1063/1.5033856},
	url = {https://doi.org/10.1063/1.5033856},
	author = {Alessandro Michelangeli and Andrea Ottolini and Raffaele Scandone}
}
@article {2017,
	title = {Krein-Visik-Birman self-adjoint extension theory revisited},
	number = {SISSA;25/2017/MATE},
	year = {2017},
	abstract = {The core results of the so-called KreIn-Visik-Birman theory of
self-adjoint extensions of semi-bounded symmetric operators are reproduced,
both in their original and in a more modern formulation, within a
comprehensive discussion that includes missing details, elucidative steps,
and intermediate results of independent interest.},
	url = {http://preprints.sissa.it/handle/1963/35286},
	author = {Matteo Gallone and Alessandro Michelangeli and Andrea Ottolini}
}
@article {2017,
	title = {Spectral Properties of the 2+1 Fermionic Trimer with Contact Interactions},
	number = {SISSA;61/2017/MATE},
	year = {2017},
	note = {Partially supported by the 2014-2017 MIUR-FIR grant \Cond-Math: Condensed Matter and
Mathematical Physics" code RBFR13WAET (S.B., A.M., A.O.), by the DAAD International
Trainership Programme (S.B.), and by a 2017 visiting research fellowship at the International Center for Mathematical Research CIRM, Trento (A.M.).},
	publisher = {SISSA},
	abstract = {We qualify the main features of the spectrum of the Hamiltonian of
point interaction for a three-dimensional quantum system consisting of three
point-like particles, two identical fermions, plus a third particle of different
species, with two-body interaction of zero range. For arbitrary magnitude of
the interaction, and arbitrary value of the mass parameter (the ratio between
the mass of the third particle and that of each fermion) above the stability
threshold, we identify the essential spectrum, localise and prove the finiteness
of the discrete spectrum, qualify the angular symmetry of the eigenfunctions,
and prove the monotonicity of the eigenvalues with respect to the mass parameter.
We also demonstrate the existence of bound states in a physically
relevant regime of masses.},
	url = {http://preprints.sissa.it/handle/1963/35303},
	author = {Simon Becker and Alessandro Michelangeli and Andrea Ottolini}
}
@article {2016,
	title = {Multiplicity of self-adjoint realisations of the (2+1)-fermionic model of Ter-Martirosyan--Skornyakov type},
	number = {SISSA;65/2016/MATE},
	year = {2016},
	abstract = {We reconstruct the whole family of self-adjoint Hamiltonians of Ter-Martirosyan-
Skornyakov type for a system of two identical fermions coupled with a third particle
of different nature through an interaction of zero range. We proceed through an
operator-theoretic approach based on the self-adjoint extension theory of Krein,
Vi{\v s}iik, and Birman. We identify the explicit {\textquoteleft}Krein-Vi{\v s}ik-Birman extension param-
eter{\textquoteright} as an operator on the {\textquoteleft}space of charges{\textquoteright} for this model (the {\textquoteleft}Krein space{\textquoteright}) and
we come to formulate a sharp conjecture on the dimensionality of its kernel. Based
on our conjecture, for which we also discuss an amount of evidence, we explain the
emergence of a multiplicity of extensions in a suitable regime of masses and we re-
produce for the first time the previous partial constructions obtained by means of
an alternative quadratic form approach.},
	url = {http://urania.sissa.it/xmlui/handle/1963/35267},
	author = {Alessandro Michelangeli and Andrea Ottolini}
}
@article {2016,
	title = {On point interactions realised as Ter-Martirosyan-Skornyakov Hamiltonians},
	number = {SISSA;11/2016/MATE},
	year = {2016},
	abstract = {For quantum systems of zero-range interaction we discuss the mathematical scheme within which modelling the two-body interaction by means of the physically relevant ultra-violet asymptotics known as the {\textquoteleft}{\textquoteleft}Ter-Martirosyan--Skornyakov condition{\textquoteright}{\textquoteright} gives rise to a self-adjoint realisation of the corresponding Hamiltonian. This is done within the self-adjoint extension scheme of Krein, Visik, and Birman. We show that the Ter-Martirosyan--Skornyakov asymptotics is a condition of self-adjointness only when is imposed in suitable functional spaces, and not just as a point-wise asymptotics, and we discuss the consequences of this fact on a model of two identical fermions and a third particle of different nature.},
	url = {http://urania.sissa.it/xmlui/handle/1963/35195},
	author = {Alessandro Michelangeli and Andrea Ottolini}
}
