Related papers: Absolute continuity of spectral shift

Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonical systems). We prove a number of Szeg\H{o}-type theorems for…

In this paper we study the $\nu$-continuity of the spectrum and some of its parts. We show that the approximate point spectrum $\sigma_{ap}$ is upper semi-$\nu$-continuous at every Fredholm operator, then we give sufficient conditions to…

In this note it is shown that for trace-class perturbations of self-adjoint operators the singular part of the spectral shift function is additive.

Using boundary triples, we develop an abstract framework to investigate the complete non-selfadjointness of the maximally dissipative extensions of dissipative operators of the form $S+iV$, where $S$ is symmetric with equal finite defect…

In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint…

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the K\"all\'en-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are…

The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self-adjoint and maximal dissipative operators. They cover both…

In this work, we give a description of Taylor spectrum of commuting 2- contractions in terms of characteristic functions of such contractions.The case of a single obtained by B.Sz.Nagy and C. Foias is generalised in this work.

We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.

The classical Weyl-von Neumann theorem states that for any self-adjoint operator $A$ in a separable Hilbert space $\mathfrak H$ there exists a (non-unique) Hilbert-Schmidt operator $C = C^*$ such that the perturbed operator $A+C$ has purely…

We consider substitutions on compact alphabets and provide sufficient conditions for the diffraction to be pure point, absolutely continuous and singular continuous. This allows one to construct examples for which the Koopman operator on…

We provide a concise, yet fairly complete discussion of the concept of essential closures of subsets of the real axis and their intimate connection with the topological support of absolutely continuous measures. As an elementary application…

Transfer operators and Ruelle zeta functions for super-continuous functions on one-sided topological Markov shifts are considered. For every super-continuous function, we construct a Banach space on which the associated transfer operator is…

This paper extends the trace formulas of [5] with perturbations in normed ideals of $B(H)$ to multivariate functions of commuting contractions admitting a dilation to commuting normal contractions.

We review a geometric approach to proving absolutely continuous (ac) spectrum for random and deterministic Schr\"odinger operators developed in \cite{FHS1,FHS2,FHS3,FHS4}. We study decaying potentials in one dimension and present a…

In this paper, we prove that for any $d$-frequency analytic quasiperiodic Schr\"odinger operator, if the frequency is weak Liouvillean, and the potential is small enough, then the corresponding operator has absolutely continuous spectrum.…

The quaternionic spectral theorem has already been considered in the literature, see e.g. [22], [31], [32], however, except for the finite dimensional case in which the notion of spectrum is associated to an eigenvalue problem, see [21], it…

We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark…

In (J. Funct. Anal. 257, 1092-1132 (2009)), Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbations is Hilbert-Schmidt. In this article, we…

We discuss spectral properties of the one-dimensional Schr\"odinger operator with a potential of the form $\sum V(n)\delta(x-n)$. Our main result says that the absolutely continuous spectum of such an operator covers an interval…