13 Citations
On the Self-Adjointness of H+A∗+A
- Mathematics
- 2020
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
- MathematicsInverse 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
- MathematicsProceedings 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
- MathematicsAnalysis 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
- MathematicsJournal 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
- Mathematics
- 2019
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
Self-adjoint Extensions of Restrictions
- Mathematics
- 2007
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
- MathematicsJournal 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
- Mathematics
- 2000
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…
Self-adjoint extensions by additive perturbations
- Mathematics
- 2001
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
- Mathematics
- 2000
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
- Mathematics
- 2001
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
- Mathematics
- 2003
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,…