Related papers: Scattering matrices and Weyl functions

We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…

Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in…

We consider a special scattering experiment with n particles in $\mathbb{R}^{n-3,1}$. The scattering equations in this set-up become the saddle-point equations of a Penner-like matrix model, where in the large $n$ limit, the spectral curve…

We study scattering for the couple $(A_{F},A_{0})$ of Schr\"odinger operators in $L^2(\mathbb{R}^3)$ formally defined as $A_0 = -\Delta + \alpha\, \delta_{\pi_0}$ and $A_F = -\Delta + \alpha\, \delta_{\pi_F}$, $\alpha >0$, where…

It is a classical result that the Weyl function of a simple symmetric operator in a Hilbert space determines a boundary triple uniquely up to unitary equivalence. We generalize this result to a simple symmetric operator in a Pontryagin…

Spectral properties of 1-D Schr\"odinger operators $\mathrm{H}_{X,\alpha}:=-\frac{\mathrm{d}^2}{\mathrm{d} x^2} + \sum_{x_{n}\in X}\alpha_n\delta(x-x_n)$ with local point interactions on a discrete set $X=\{x_n\}_{n=1}^\infty$ are well…

Let $A$ be a densely defined simple symmetric operator in $\gH$, let $\Pi=\bt$ be a boundary triplet for $A^*$ and let $M(\cd)$ be the corresponding Weyl function. It is known that the Weyl function $M(\cd)$ determines the boundary triplet…

We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems involving systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…

Self-adjoint Schr\"odinger operators with $\delta$ and $\delta'$-potentials supported on a smooth compact hypersurface are defined explicitly via boundary conditions. The spectral properties of these operators are investigated, regularity…

Let $A$ be a densely defined symmetric operator with equal deficiency indices in a Hilbert space. We introduce the notion of a Weyl function $M(z)$ of $A$ corresponding to an ordinary boundary triplet of the operator $A^*$ and then…

We examine two kinds of spectral theoretic situations: First, we recall the case of self-adjoint half-line Schr\"odinger operators on $[a,\infty)$, $a\in\mathbb{R}$, with a regular finite end point $a$ and the case of Schr\"odinger…

In this work we construct the model of a skew--selfadjoint operator with a simple spectrum acting on a Hilbert quaternion bimodule. This result is based on the Spectral Theorem for a skew--selfadjoint operator.

We study stationary scattering for Schr\"odinger operators in $\mathbb R^3$ with finitely many concentric $\delta$--shell interactions of constant real strengths. Starting from the self--adjoint realization and the boundary resolvent…

The object of study in this paper is the on-shell scattering matrix $S(E)$ of the Schr\"odinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of $S(E)$ in the…

The matrix-valued Weyl-Titchmarsh functions $M(\lambda)$ of vector-valued Sturm-Liouville operators on the unit interval with the Dirichlet boundary conditions are considered. The collection of the eigenvalues (i.e., poles of $M(\lambda)$)…

We consider scattering matrix for Schr\"odinger-type operators on $\mathbb{R}^d$ with perturbation $V(x)=O(\langle x\rangle^{-1})$ as $|x|\to\infty$. We show that the scattering matrix (with time-independent modifiers) is a…

We study two- and three-dimensional matrix Schr\"odinger operators with $m\in \mathbb N$ point interactions. Using the technique of boundary triplets and the corresponding Weyl functions, we complete and generalize the results obtained by…

We show that the scattering matrix for a class of Schr\"odinger-type operators with long-range perturbations is a Fourier integral operator with the phase function which is the generating function of the modified classical scattering map.

Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the Weyl M-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we…

We apply both the theory of boundary triples and perturbation theory to the setting of semi-bounded Sturm-Liouville operators with two limit-circle endpoints. For general boundary conditions we obtain refined and new results about their…