Related papers: Higher-Order Trace Formulas for Contractive and Di…

In this paper we study a class of Jacobi operators, such that each operator is generated by the unit Borel measure with a support consisting of a finite number of intervals on the real line R and a finite number of points in C, located…

For every symmetrically normed ideal $\mathcal{E}$ of compact operators, we give a criterion for the existence of a continuous singular trace on $\mathcal{E}$. We also give a criterion for the existence of a continuous singular trace on…

Let $f$ be a function on ${\Bbb R}^2$ in the inhomogeneous Besov space $B_{\infty,1}^1({\Bbb R}^2)$. For a pair $(A,B)$ of not necessarily bounded and not necessarily commuting self-adjoint operators, we define the function $f(A,B)$ of $A$…

Suzuki-Trotter decompositions of exponential operators like $\exp(Ht)$ are required in almost every branch of numerical physics. Often the exponent under consideration has to be split into more than two operators $H=\sum_k A_k$, for…

This article is a continuation of our work on generalized matrix-weighted Besov--Triebel--Lizorkin-type spaces with matrix $\mathcal{A}_{\infty}$ weights. In this article, we establish the boundedness of pseudo-differential, trace, and…

We consider 3-dim Schr\"odinger operators with a complex potential. We obtain new trace formulas. In order to prove these results we study analytic properties of a modified Fredholm determinant. In fact we reformulate spectral theory…

We determine the trace formula for the fourth order operator on the circle. This formula is similar to the famous trace formula for the Hill operator obtained by Dubrovin, Its-Matveev and McKean-van Moerbeke.

Borg-type uniqueness theorems for matrix-valued Jacobi operators H and supersymmetric Dirac difference operators D are proved. More precisely, assuming reflectionless matrix coefficients A, B in the self-adjoint Jacobi operator H=AS^+ +…

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…

We develop a sharp boundary trace theory in arbitrary bounded Lipschitz domains which, in contrast to classical results, allows "forbidden" endpoints and permits the consideration of functions exhibiting very limited regularity. This is…

Recurrence and explicit formulae for contractions (partial traces) of antisymmetric and symmetric products of identical trace class operators are derived. Contractions of product density operators of systems of identical fermions and bosons…

This note is an extension of a recent work on the analytical bootstrapping of $O(N)$ models. An additonal feature of the $O(N)$ model is that the OPE contains trace and antisymmetric operators apart from the symmetric-traceless objects…

We investigate trace formulas for Jacobi operators which are trace class perturbations of quasi-periodic finite-gap operators using Krein's spectral shift theory. In particular we establish the conserved quantities for the solutions of the…

We show that the space of trace-class operators on a Hilbert module over a commutative C*-algebra, as defined and studied in earlier work of Stern and van Suijlekom (Journal of Functional Analysis, 2021), is completely isometrically…

Let $A$ be a selfadjoint operator in a separable Hilbert space, $K$ a selfadjoint Hilbert-Schmidt operator, and $f\in C^n(\mathbb{R})$. We establish that $\varphi(t)=f(A+tK)-f(A)$ is $n$-times continuously differentiable on $\mathbb{R}$ in…

This paper introduces a new approach to the non-normal Dixmier and Connes-Dixmier traces (introduced by Dixmier and adapted to non-commutative geometry by Connes) on a general Marcinkiewicz space associated with an arbitrary semifinite von…

In this paper we explore a certain class of non-selfadjoint operators acting in a complex separable Hilbert space. We consider a perturbation of a non-selfadjoint operator by an operator that is also non-selfadjoint. Our consideration is…

We consider the difference $f(-\Delta +V)-f(-\Delta)$ of functions of Schr\"odinger operators in $L^2(\mathbb R^d)$ and provide conditions under which this difference is trace class. We are particularly interested in non-smooth functions…

We consider Schr\"odinger operators with complex-valued decreasing potentials on the half-line. Such operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the…

Weyl-von Neumann Theorem asserts that two bounded self-adjoint operators $A,B$ on a Hilbert space $H$ are unitarily equivalent modulo compacts, i.e., $uAu^*+K=B$ for some unitary $u\in \mathcal{U}(H)$ and compact self-adjoint operator $K$,…