Related papers: Determinants of Classical SG-Pseudodifferential Op…

Using a global symbol calculus for pseudodifferential operators on tori, we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols. We…

Based on the notion of the resolvent and on the Hilbert identities, this paper presents a number of classical results in the theory of differential operators and some of their applications to the theory of automorphic functions and number…

Given a cone pseudodifferential operator $P$ we give a full asymptotic expansion as $t\to 0^+$ of the trace $\Tr Pe^{-tA}$, where $A$ is an elliptic cone differential operator for which the resolvent exists on a suitable region of the…

The classical Szeg\"o theorems study the asymptotic behaviour of the determinants of the finite sections $P_n T(a) P_n$ of Toeplitz operators, i.e., of operators which have constant entries along each diagonal. We generalize these results…

We define the Wodzicki Residue TR(A) for A in a space of operators with double order (m_1,m_2). Such operators are globally defined initially on R^n and then, more generally, on a class of non-compact manifolds, namely, the manifolds with…

As it is shown in previous works, discrete periodic operators with defects are unitarily equivalent to the operators of the form $$ {\mathcal A}{\bf u}={\bf A}_0{\bf u}+{\bf A}_1\int_0^1dk_1{\bf B}_1{\bf u}+...+{\bf…

In work of C. A. Tracy and the author asymptotic formulas were derived for certain operator determinants which gave solutions to the cylindrical Toda equations. Later the author considered a more general class of operators which retained…

Let $(M,g)$ be a compact smoothly stratified pseudomanifold with an iterated cone-edge metric satisfying a spectral Witt condition. Under these assumptions the Hodge-Laplacian $\Delta$ is essentially self-adjoint. We establish the…

Let M be a closed manifold and let CL(M) be the algebra of classical pseudodifferential operators. The aim of this note is to classify trace functionals on the subspaces CL^a(M) of CL(M) of operators of order a. CL^a(M) is a CL^0(M)-module…

Let $\gp$ be a finite group acting on a compact manifold $M$ and $\maA(M)$ denote the algebra of classical complete symbols on $M$. We determine all traces on the cross-product algebra $\maA(M) \rtimes \Gamma$. These traces appear as…

We show that the Szego regularized determinant of a zeroth order operator differs from the zeta regularized determinant of the same operator by a local term. In addition, we compute multiplicative anomalies for the zeta regularized…

We construct a parametrix of a resolvent of elliptic differential operators acting on half-densities on manifolds with ends. The construction is carried out by introducing suitable pseudodifferential operators compatible with the end…

In this paper we introduce and study pseudo-differential operators with operator valued symbols on the abstract Heisenberg group $\mathbb{H}(G):=G \times \widehat{G} \times \mathbb{T},$ where $G$ a locally compact abelian group with its…

We establish Plemelj-Smithies formulas for determinants in different algebras of operators. In particular we define a Poincar\'e type determinant for operators on the torus $\Tn$ and deduce formulas for determinants of periodic…

We consider Sturm-Liouville operators on the line segment [0, 1] with general regular singular potentials and separated boundary conditions. We establish existence and a formula for the associated zeta-determinant in terms of the Wronski-…

We use the boundary triplet approach to extend the classical concept of perturbation determinants to a more general setup. In particular, we examine the concept of perturbation determinants to pairs of proper extensions of closed symmetric…

We present a new multiparameter resolvent trace expansion for elliptic operators, polyhomogeneous in both the resolvent and auxiliary variables. For elliptic operators on closed manifolds the expansion is a simple consequence of the…

Let R be a ring with a derivation \delta. In this paper, we prove that an analogue of Amitsur's property holds for left T-nilpotent radideals of pseudo-differential operator rings R((x^{-1}; \delta)), where R is a delta-compatible ring. As…

The principal aim in this paper is to employ a recently developed unified approach to the computation of traces of resolvents and $\zeta$-functions to efficiently compute values of spectral $\zeta$-functions at positive integers associated…

An operator $H=H_{0}+V$ where $H_{0}=i^{-N} \partial^{N}$ ($N$ is arbitrary) and $V$ is a differential operator of order $N-1$ with coefficients decaying sufficiently rapidly at infinity is considered in the space $L^2(\Bbb R)$. The goal of…