We consider two calculi of pseudodifferential operators on manifolds with fibered boundary: Mazzeo’s edge calculus, which has as local model the operators associated to products of closed manifolds with asymptotically hyperbolic spaces, and the φ calculus of Mazzeo and the second author, which is similarly modeled on products of closed manifolds with asymptotically Euclidean spaces. We construc...

We consider two calculi of pseudodifferential operators on manifolds with fibered boundary: Mazzeo’s edge calculus, which has as local model the operators associated to products of closed manifolds with asymptotically hyperbolic spaces, and the φ calculus of Mazzeo and the second author, which is similarly modeled on products of closed manifolds with asymptotically Euclidean spaces. We construc...

Manifolds with fibered hyperbolic cusp metrics include hyperbolic manifolds with cusps and locally symmetric spaces of Q-rank one. We extend Vaillant’s treatment of Dirac-type operators associated to these metrics by weaking the hypotheses on the boundary families through the use of Fredholm perturbations as in the family index theorem of Melrose and Piazza and by treating the index of families...

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...

By the introduction of a generalized Evans function defined by an appropriate 2-modified Fredholm determinant, we give a simple proof of convergence in location and multiplicity of Hill’s method for numerical approximation of spectra of periodiccoefficient ordinary differential operators. Our results apply to operators of nondegenerate type, under the condition that the principal coefficient ma...

We construct a Kato-type decomposition of quasi-Fredholm operators on Banach spaces. This generalizes the corresponding result of Labrousse for Hilbert space operators. The result is then applied to B-Fredholm operators. Denote by B(X) the set of all bounded linear operators acting on a Banach space X. For T ∈ B(X) denote by N(T ) = {x ∈ X : Tx = 0} and R(T ) = TX its kernel and range, respecti...

The analytic approach to spectral flow is about ten years old. In that time it has evolved to cover an ever wider range of examples. The most critical extension was to replace Fredholm operators in the classical sense by Breuer-Fredholm operators in a semifinite von Neumann algebra. The latter have continuous spectrum so that the notion of spectral flow turns out to be rather more difficult to ...

In [24], Koliha proved that T ? L(X) (X is a complex Banach space) generalized Drazin invertible operator iff there exists an S commuting with such STS = and ?(T2S?T) {0} 0 < acc ?(T). Later, in [14, 34] the authors extended class of operators they also pseudo-Fredholm introduced by Mbekhta [27] other classes semi-Fredholm operators. As continuation these works, we introduce study 1zinvertib...

We discuss the essential self-adjointness of wave operators, as well as the limiting absorption principle, in generalizations of asymptotically Minkowski settings. This is obtained via using a Fredholm framework for inverting the spectral family first, and then refining its conclusions to show dense range of − λ, λ / ∈ R, in Lsc when acting on an appropriate subdomain.

We study the existence of a solution for a non-necessarily cooperative system of n equations involving Schrödinger operators defined on RN and we study also a limit case (the Fredholm Alternative (FA)). We derive results for semilinear systems. 2000 Mathematics Subject Classification. 35J10, 35J45.