# Asymptotic completeness and S-matrix for singular perturbations

@article{Mantile2019AsymptoticCA,
title={Asymptotic completeness and S-matrix for singular perturbations},
author={Andrea Mantile and Andrea Posilicano},
journal={Journal de Math{\'e}matiques Pures et Appliqu{\'e}es},
year={2019}
}
• Published 20 November 2017
• Mathematics
• Journal de Mathématiques Pures et Appliquées
13 Citations
Let $H:D(H)\subseteq{\mathscr F}\to{\mathscr F}$ be self-adjoint and let $A:D(H)\to{\mathscr F}$ (playing the role of the annihilator operator) be $H$-bounded. Assuming some additional hypotheses on
Inverse scattering for the Laplace operator with boundary conditions on Lipschitz surfaces
• Mathematics
Inverse Problems
• 2019
We provide a general scheme, in the combined frameworks of Mathematical Scattering Theory and Factorization Method, for inverse scattering for the couple of self-adjoint operators
Inverse wave scattering in the Laplace domain: A factorization method approach
• Mathematics
Proceedings of the American Mathematical Society
• 2020
Let $\Delta_{\Lambda}\le \lambda_{\Lambda}$ be a semi-bounded self-adjoint realization of the Laplace operator with boundary conditions (Dirichlet, Neumann, semi-transparent) assigned on the
On inverses of Krein's Q-functions
• Mathematics
• 2018
Let $A_{Q}$ be the self-adjoint operator defined by the $Q$-function $Q:z\mapsto Q_{z}$ through the Krein-like resolvent formula (-A_{Q}+z)^{-1}= (-A_{0}+z)^{-1}+G_{z}WQ_{z}^{-1}VG_{\bar
Scattering on Leaky Wires in Dimension Three
• Mathematics
Analysis and Operator Theory
• 2019
We consider the scattering problem for a class of strongly singular Schrodinger operators in $$L^2({\mathbb R}^3)$$ which can be formally written as \(H_{\alpha ,\varGamma }= -\varDelta + \delta
Optimization of the lowest eigenvalue of a soft quantum ring
• Mathematics
• 2020
We consider the self-adjoint two-dimensional Schrodinger operator $H_\mu$ associated with the differential expression $-\Delta -\mu$ describing a particle exposed to an attractive interaction given
Inverse wave scattering in the time domain for point scatterers
• Mathematics
• 2021
Abstract. Let ∆α,Y be the bounded from above self-adjoint realization in L (R) of the Laplacian with n point scatterers placed at Y = {y1, . . . , yn} ⊂ R, the parameters (α1, . . . αn) ≡ α ∈ R being
Scattering from local deformations of a semitransparent plane
• Mathematics
Journal of Mathematical Analysis and Applications
• 2019
On the Origin of Minnaert Resonances
• Mathematics
• 2021
It is well known that the presence, in a homogeneous acoustic medium, of a small inhomogeneity (of size ε ), enjoying a high contrast of both its mass density and bulk modulus, ampliﬁes the generated
Scattering of particles bounded to an infinite planar curve
Non-relativistic quantum particles bounded to a curve in R^2 by attractive contact $\delta$-interaction are considered. The interval between the energy of the transversal bound state and zero is

## References

SHOWING 1-10 OF 60 REFERENCES
We provide a simple recipe for obtaining all self-adjoint extensions, together with their resolvent, of the symmetric operator $S$ obtained by restricting the self-adjoint operator
Limiting absorption principle, generalized eigenfunctions, and scattering matrix for Laplace operators with boundary conditions on hypersurfaces
• Mathematics
Journal of Spectral Theory
• 2018
We provide a limiting absorption principle for the self-adjoint realizations of Laplace operators corresponding to boundary conditions on (relatively open parts $\Sigma$ of) compact hypersurfaces
A Krein-like Formula for Singular Perturbations of Self-Adjoint Operators and Applications
Abstract Given a self-adjoint operator A :  D ( A )⊆ H → H and a continuous linear operator τ :  D ( A )→ X with Range τ ′∩ H ′={0}, X a Banach space, we explicitly construct a family A τ Θ of
Let AN be the symmetric operator given by the restriction of A to N , where A is a self-adjoint operator on the Hilbert space H and N is a linear dense set which is closed with respect to the graph
Singular Operator as a Parameter of Self-adjoint Extensions
Let A be a symmetric restriction of a self-adjoint bounded from below operator A in a Hilbert space H and let A ∞ denote the Friedrichs extension of A. We prove that in the case, where A ∞ ≠ A, under
Zeta functions with Dirichlet and Neumann boundary conditions for exterior domains
• Mathematics
• 1996
We generalize earlier studies on the Laplacian for a bounded open domain $\Omega\in \real^2$ with connected complement and piecewise smooth boundary. We compare it with the quantum mechanical
Upper Bounds for Neumann–Schatten Norms
AbstractLet H and Haux be Hilbert spaces, H a nonnegative self-adjoint operator in H,α,s>0 and J a bounded linear transformation from the Hilbert space D(Hs/2) (equipped with the graph scalar product
Boundary triples and Weyl functions for singular perturbations of self-adjoint operators
Given the symmetric operator $A_N$ obtained by restricting the self-adjoint operator $A$ to $N$, a linear dense set, closed with respect to the graph norm, we determine a convenient boundary triple
Generalized interactions supported on hypersurfaces
• Mathematics
• 2015
We analyze a family of singular Schr\"odinger operators with local singular interactions supported by a hypersurface $\Sigma \subset \mathbb{R}^n, n \ge 2$, being the boundary of a Lipschitz domain,