We define a new topology, weaker than the gap topology, on the space of selfadjoint operators affiliated to a semifinite von Neumann algebra and define the real-valued spectral flow for a continuous path of selfadjoint Breuer-Fredholm operators in terms of a generalization of the winding number. We compare our definition with Phillips’ analytical definition. Furthermore we prove the homotopy in...

The classical concept of Q-functions associated to symmetric and selfadjoint operators due to M.G. Krein and H. Langer is extended in such a way that the Dirichlet-to-Neumann map in the theory of elliptic differential equations can be interpreted as a generalized Q-function. For couplings of uniformly elliptic second order differential expression on bounded and unbounded domains explicit Krein ...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

Let P be a selfadjoint elliptic operator of order m > 0 acting on the sections of a Hermitian vector bundle over a compact Riemannian manifold of dimension n. General arguments show that its zeta and eta functions may have poles only at points of the form s = k m , where k ranges over all non-zero integers ≤ n. In this paper, we construct elementary and explicit examples of perturbations of P w...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

Limiting absorption principle is justified for second-order selfadjoint elliptic operators in two-dimensional spaces.

The nonlocal boundary value problems for differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valued Lp-spaces of these problems are given. By using these results, the maximal regularit...

We compare various topologies on the space of (possibly unbounded) Fredholm selfadjoint operators and explain their K-theoretic relevance.∗ Introduction The work of Atiyah and Singer on the index of elliptic operators on manifolds has singled out the role of the space of bounded Fredholm operators in topology. It is a classifying space for a very useful functor, the topological K-theory. This m...