Adiabatic vacuum states are a well-known class of physical states for linear quantum fields on Robertson-Walker spacetimes. We extend the definition of adiabatic vacua to general spacetime manifoldsâ€¦ (More)

Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M , whose (complex) order is not an integer greaterâ€¦ (More)

Given a manifold B with conical singularities, we consider the cone algebra with discrete asymptotics, introduced by Schulze, on a suitable scale of Lp-Sobolev spaces. Ellipticity is proven to beâ€¦ (More)

Johannes Aastrup, Severino T. Melo, Bertrand Monthubert, Elmar Schrohe

2006

Can Boutet de Monvelâ€™s algebra on a compact manifold with boundary be obtained as the algebra Î¨(G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principalâ€¦ (More)

We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted Lp-spaces over B, 1 < p <â€¦ (More)

Let X be a smooth manifold with boundary of dimension n > 1. The operators of order ?n and type zero in Boutet de Monvel's calculus form a subset of Dixmier's trace ideal L

We derive conditions that ensure the existence of a bounded Hâˆž-calculus in weighted Lp-Sobolev spaces for closed extensions A T of a differential operator A on a conic manifold with boundary, subjectâ€¦ (More)

For manifolds with boundary, we define an extension of Wodzickiâ€™s noncommutative residue to boundary value problems in Boutet de Monvelâ€™s calculus. We show that this residue can be recovered with theâ€¦ (More)

We consider edge-degenerate families of pseudodiierential boundary value problems on a semi-innnite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone nearâ€¦ (More)

We construct spectral triples for the Sierpinski gasket as infinite sums of unbounded Fredholm modules associated with the holes in the gasket and investigate their properties. For each element inâ€¦ (More)