Related papers: The Witten index and the spectral shift function

The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…

The spectral eta-invariant of a self-adjoint elliptic differential operator on a closed manifold is rigid, provided that the parity of the order is opposite to the parity of dimension of the manifold. The paper deals with the calculation of…

Our goal is to extend the theory of the spectral shift function to the case where only the difference of some powers of the resolvents of self-adjoint operators belongs to the trace class. As an example, we consider a couple of Dirac…

We consider the Dirac operator on asymptotically static Lorentzian manifolds with an odd-dimensional compact Cauchy surface. We prove that if Atiyah-Patodi-Singer boundary conditions are imposed at infinite times then the Dirac operator is…

Let $D_t$, $t \in [0,1]$ be an arbitrary 1-parameter family of Dirac type operators on a two-dimensional disk with $m-1$ holes. Suppose that all operators $D_t$ have the same symbol, and that $D_1$ is conjugate to $D_0$ by a scalar gauge…

We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of m complex-valued half-densities over a connected compact n-dimensional manifold without boundary. The eigenvalues of the principal symbol are…

In the first half of this text we explore the interrelationships between the abstract theory of limit operators (see e.g. the recent monographs of Rabinovich, Roch & Silbermann and Lindner) and the concepts and results of the generalised…

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…

We revisit an argument due to Lesch (Topology 32 (1993), no. 3, 611-623) for proving the cobordism invariance of the index of Dirac operators on even-dimensional closed manifolds and combine this with recent work by the author (New York J.…

This paper is devoted to mathematical and physical properties of the Dirac operator and spectral geometry. Spin-structures in Lorentzian and Riemannian manifolds, and the global theory of the Dirac operator, are first analyzed. Elliptic…

For bounded right linear operators, in a right quaternionic Hilbert space with a left multiplication defined on it, we study the approximate $S$-point spectrum. In the same Hilbert space, then we study the Fredholm operators and the…

We define a new topology, weaker than the gap topology, on the space of selfadjoint unbounded operators on a separable Hilbert space. We show that the subspace of selfadjoint Fredholm operators represents the functor $K^1$ from the category…

Let $G$ be a compact Lie group acting smoothly on a smooth, compact manifold $M$, let $P \in \psi^m(M; E_0, E_1)$ be a $G$--invariant, classical pseudodifferential operator acting between sections of two vector bundles $E_i \to M$, $i =…

We show that a recent spectral flow approach proposed by Berkolaiko-Cox-Marzuola for analyzing the nodal deficiency of the nodal partition associated to an eigenfunction can be extended to more general partitions. To be more precise, we…

The extended Heisenberg algebra for a contact manifold has a symbolic calculus that accommodates both Heisenberg pseudodifferential operators as well as classical pseudodifferential operators. We derive here a formula for the index of…

We affirmatively settle the question on existence of a real-valued higher order spectral shift function for a pair of self-adjoint operators $H$ and $V$ such that $V$ is bounded and $V(H-iI)^{-1}$ belongs to a Schatten-von Neumann ideal…

We develop by example a type of index theory for non-Fredholm operators. A general framework using cyclic homology for this notion of index was introduced in a separate article [CaKa13] where it may be seen to generalise earlier ideas of…

We give an elementary solution of the index problem for elliptic operators associated with the shift operator along the trajectories of an isometric diffeomorphism of a closed smooth manifold. This solution is based on a reduction (which…

We offer a spectral analysis for a class of transfer operators. These transfer operators arise for a wide range of stochastic processes, ranging from random walks on infinite graphs to the processes that govern signals and recursive wavelet…

We consider operators in the domains with the boundaries and derive sharp spectral asymptotics (containing non-Weyl correction) in the case when Hamiltonian flow is periodic. Even if operator is scalar but not second order (or even…