相关论文: Trace Formulas for Schroedinger Operators in Conne…
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…
The discrete spectra of certain two-dimensional Schrodinger operators are numerically calculated. These operators have interesting spectral properties, i.e. their kernels are multi-dimensional and the deformations of potentials via the…
We consider a compact Riemann surface $\mathscr{R}$ with a complex of non-intersecting Jordan curves, whose complement is a pair of Riemann surfaces with boundary, each of which may be possibly disconnected. We investigate conformally…
Koplienko \cite{Ko} found a trace formula for perturbations of self-adjoint operators by operators of Hilbert-Schmidt class $\mathcal{B}_2(\mathcal{H})$. Later, Neidhardt introduced a similar formula in the case of pair of unitaries…
In this paper, we extend the class of admissible functions for the trace formula of the second order in the self-adjoint, unitary, and contraction cases for a perturbation in the Hilbert-Schmidt class $\mathcal{S}^2(\mathcal{H})$ by…
We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fr\'echet…
Spectral properties of Schr\"odinger operators on compact metric graphs are studied and special emphasis is put on differences in the spectral behavior between different classes of vertex conditions. We survey recent results especially for…
The present paper is devoted to studying the Hill-type formula and Krein-type trace formula for ODE, which is a continuous work of our previous work for Hamiltonian systems \cite{HOW}. Hill-type formula and Krein-type trace formula are…
I apply the set-up of Lax-Phillips Scattering Theory to a non-archimedean local field. It is possible to choose the outgoing space and the incoming space to be Fourier transforms of each other. Key elements of the Lax-Phillips theory are…
Given a self-adjoint operator H, a self-adjoint trace class operator V and a fixed Hilbert-Schmidt operator F with trivial kernel and co-kernel, using limiting absorption principle an explicit set of full Lebesgue measure is defined such…
We study spectral theory for the Schrodinger operator on manifolds possessing an escape function. A particular class of examples are manifolds with Euclidean and/or hyperbolic ends.
We consider discrete Schr\"odinger operators with real periodic potentials on periodic graphs. The spectra of the operators consist of a finite number of bands. By "rolling up" a periodic graph along some appropriate directions we obtain…
In this article we continue our analysis of Schroedinger operators with a random potential using scattering theory. In particular the theory of Krein's spectral shift function leads to an alternative construction of the density of states in…
The main objective of this paper is to systematically develop a spectral and scattering theory for selfadjoint Schr\"odinger operators with $\delta$-interactions supported on closed curves in $\mathbb R^3$. We provide bounds for the number…
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the…
We consider perturbations of quasi-periodic Schr\"odinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the…
We formulate the inverse spectral theory of infinite gap Hill's operators with bounded periodic potential as a Riemann--Hilbert problem on a typically infinite collection of spectral bands and gaps. We establish a uniqueness theorem for…
\We consider an inverse scattering problem for Schr\"odinger operators with energy dependent potentials. The inverse problem is formulated as a Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for two distinct…
We survey results concerning the spectral properties of limit-periodic operators. The main focus is on discrete one-dimensional Schr\"odinger operators, but other classes of operators, such as Jacobi and CMV matrices, continuum…
Schr\"{o}dinger operators with nonlocal $\delta$-interaction are studied with the use of the Lax-Phillips scattering theory methods. The condition of applicability of the Lax-Phillips approach in terms of non-cyclic functions is…