相关论文: Scattering matrices and Weyl functions
We extend the notion of generalized boundary triples and their Weyl functions from extension theory of symmetric operators to adjoint pairs of operators, and we provide criteria on the boundary parameters to induce closed operators with a…
We establish a semiclassical trace formula in a general framework of microhyperbolic hermitian systems of $h$-pseudodifferential operators, and apply it to the study of the spectral shift function associated to a pair of selfadjoint…
We investigate the connections between Weyl-Titchmarsh-Kodaira theory for one-dimensional Schr\"odinger operators and the theory of $n$-entire operators. As our main result we find a necessary and sufficient condition for a one-dimensional…
For any positive real number $s$, we study the scattering theory in a unified way for the fractional Schr\"{o}dinger operator $H=H_0+V$, where $H_0=(-\Delta)^\frac s2$ and the real-valued potential $V$ satisfies short range condition. We…
We consider operators of the form $\mathbf{T}=\mathbf{A^*}(V\mu)\mathbf{A}$ in $\mathbb{R}^\mathbf{N}$, where $\mathbf{A}$ is a pseudodifferential operator of order $-l$, $\mu$ is a compactly supported singular measure, order $s>0$…
The solution of the scattering problem based on the Lippmann-Schwinger equation requires in many cases a discretization of the spectrum in the continuum which does not respect the unitary equivalence of the S-matrix on the finite grid. We…
In this paper we study direct and inverse problems for discrete and continuous time skew-selfadjoint Dirac systems with rectangular (possibly non-square) pseudo-exponential potentials. For such a system the Weyl function is a strictly…
The notion of quasi boundary triples and their Weyl functions from extension theory of symmetric operators is extended to the general framework of adjoint pairs of operators under minimal conditions on the boundary maps. With the help of…
An obstacle $K \subset \R^n,\: n \geq 3,$ $n$ odd, is called trapping if there exists at least one generalized bicharacteristic $\gamma(t)$ of the wave equation staying in a neighborhood of $K$ for all $t \geq 0.$ We examine the…
The matrix Sturm-Liouville operator on a finite interval with the boundary conditions in the general self-adjoint form and with the singular potential from the class $W_2^{-1}$ is studied. This operator generalizes Sturm-Liouville operators…
We continue the study of boundary data maps, that is, generalizations of spectral parameter dependent Dirichlet-to-Neumann maps for (three-coefficient) Sturm-Liouville operators on the finite interval $(a,b)$, to more general boundary…
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
In this study, singular diffusion operator with jump conditions is considered. Integral representations have been derived for solutions that satisfy boundary conditions and jump conditions. Some properties of eigenvalues and eigenfunctions…
We discuss a few integral operators and provide expressions for them in terms of smooth functions of some natural self-adjoint operators. These operators appear in the context of scattering theory, but are independent of any perturbation…
A scattering process can be described by suitably closing the system and considering the first return map from the entrance onto itself. This scattering map may be singular and discontinuous, but it will be measure preserving as a…
We analyse the scattering operator associated with the defocusing nonlinear Schr{\"o}dinger equation which captures the evolution of solutions over an infinite time-interval under the nonlinear flow of this equation. The asymptotic nature…
We study spectral properties of the Carleman operator (the Hankel operator with kernel $h_{0}(t)=t^{-1}$) and, in particular, find an explicit formula for its resolvent. Then we consider perturbations of the Carleman operator $H_{0}$ by…
The spectrum of a selfadjoint second order elliptic differential operator in $L^2(\mathbb{R}^n)$ is described in terms of the limiting behavior of Dirichlet-to-Neumann maps, which arise in a multi-dimensional Glazman decomposition and…
We present a new theory of photoemission for Weyl semimetals. We derive this theory using a model with a boundary surface at $z=0$. Due to the boundary, the self adjoint condition needs to be verified in order to ensure physical solutions.…
We develop the analytic perturbation technique on the absolutely continuous spectrum and calculate the Scattering matrix for the Schr\"{o}dinger operator on the Quantum Network based on the Dirichlet-to Neumann map of an Intermediate…