Related papers: On formula of regularized traces II
Let $G$ be a compact Lie group acting on a compact complex manifold $M$. We prove a trace density formula for the $G$-Lefschetz number of a differential operator on $M$. We generalize Engeli and Felder's recent results to orbifolds.
Two trace formulas for the spectra of arbitrary Hermitian matrices are derived by transforming the given Hermitian matrix $H$ to a unitary analogue. In the first type the unitary matrix is $e^{i(\lambda\II - H)}$ where $\lambda$ is the…
We study the computational complexity of estimating the normalized trace $2^{-n}Tr[f(A)]$ for a log-local Hamiltonian $A$ acting on $n$ qubits. This problem arises naturally in the DQC1 model, yet its complexity is only understood for a…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
We consider a general second order matrix operator in a multi-dimensional domain subject to a classical boundary condition. This operator is perturbed by a first order differential operator, the coefficients of which depend arbitrarily on a…
We extend the well-known trace formula for Hill's equation to general one-dimensional Schr\"odinger operators. The new function $\xi$, which we introduce, is used to study absolutely continuous spectrum and inverse problems.
We consider a variable order differential operator on a graph with a cycle. We study the inverse spectral problem for this operator by the system of spectra. The main results of the paper are the uniqueness theorem and the constructive…
We present some results on the monotonicity of some traces involving functions of self-adjoint operators with respect to the natural ordering of their associated quadratic forms. We also apply these results to complete a proof of the Wegner…
In this note we give a simplified ordinal analysis of first-order reflection. An ordinal notation system $OT$ is introduced based on $\psi$-functions. Provable $\Sigma_{1}$-sentences on $L_{\omega_{1}^{CK}}$ are bounded through…
The aim of this paper is twofold: On one hand we discuss an abstract approach to symmetrized Fredholm perturbation determinants and an associated trace formula for a pair of operators of positive-type, extending a classical trace formula.…
In this note we give a brief survey of the most elementary criteria used to determine the surjectivity of the trace operator on the ring of integers of a number field $K$. Furthermore, we introduce an easy to state yet unknown surjectivity…
We provide sufficient conditions under which the difference of the resolvents of two higher-order operators acting in $\R^N$ belongs to trace classes $\cC^p$. We provide explicit estimates on the norm of the resolvent difference in terms of…
In recent years, higher-order trace formulas of operator functions have attracted considerable attention to a large part of the perturbation theory community. In this direction, we prove estimates for traces of higher-order derivatives of…
For weighted Bergman spaces on the unit disk, we give trace formulas of semicommutators of Toeplitz operators with $\mathscr{C}^2(\overline{\mathbb{D}})$ symbols. We generalize this formula to weighted Bergman spaces on the unit ball in…
In the abstract pseudodifferential setup of Connes and Moscovici, we prove a general formula for the discrepancies of zeta-regularised traces associated with certain spectral triples, and we introduce a canonical trace on operators, whose…
We give a rigorous version of the classical Balian-Bloch trace formula, a semiclassical expansion around a periodic reflecting ray of the (regularized) resolvent of the Dirichlet Laplacian on a bounded smooth plane domain. It is equivalent…
We construct a functional model for rank one perturbations of compact normal operators acting in a certain Hilbert spaces of entire functions generalizing de Branges spaces. Using this model we study completeness and spectral synthesis…
In this paper we give a trace formula for Hecke operators acting on the cohomology of a Fuchsian group of finite covolume, with coefficients in a module $V$. The proof is based on constructing an operator whose trace on $V$ equals the…
We prove the validity of regularizing properties of a double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with constant coefficients in Schauder spaces by…
I offer a simple and useful formula for the resolvent of a small rank perturbation of large matrices. I discuss applications of this formula, in particular, to analytical and numerical solving of difference boundary value problems. I…