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- Elmar Schrohe, Jj Org Seiler
- 2007

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 be equivalent to the Fredholm property in these spaces; it turns out to be independent of the choice of p. We then show that the cone algebra is closed under… (More)

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 manifolds by using the notion of the Sobolev wavefront set. This definition is also applicable to interacting field theories. Hadamard states form a special subclass of… (More)

- S T Melo, R Nest, E Schrohe
- 2001

We consider the norm closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a manifold X with boundary ∂X. We first describe the image and the kernel of the continuous extension of the boundary principal symbol homomorphism to A. If X is connected and ∂X is not empty, we then show that the K-groups of A are… (More)

- L Maniccia, E Schrohe, J Seiler
- 2008

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 greater than or equal to − dim M , is the unique functional which (i) is linear on its domain, (ii) has the trace property and (iii) coincides with the L 2-operator… (More)

- Johannes Aastrup, Elmar Schrohe
- 2005

For a smooth manifold X with boundary we construct a semigroupoid T − X and a continuous field C * r (T − X) of C *-algebras which extend Connes' construction of the tangent groupoid. We show the asymptotic multiplicativity of-scaled truncated pseudodifferential operators with smoothing symbols and compute the K-theory of the associated symbol algebra.

- J Aastrup, S T Melo, B Monthubert, E Schrohe
- 2006

Can Boutet de Monvel's algebra on a compact manifold with boundary be obtained as the algebra Ψ 0 (G) of pseudodifferential operators on some Lie groupoid G? If it could, the kernel G of the principal symbol homomorphism would be isomorphic to the groupoid C *-algebra C * (G). While the answer to the above question remains open, we exhibit in this paper a… (More)

- Severino T. Melo, Thomas Schick, Elmar Schrohe
- 2004

We study the C *-closure A of the algebra of all operators of order and class zero in Boutet de Monvel's calculus on a compact connected manifold X with boundary ∂X = ∅. We find short exact sequences in K-theory which split, so that Ki(A/K) ∼ = Ki(C(X))⊕K1−i(C0(T * X •)). Using only simple K-theoretic arguments and the Atiyah-Singer Index Theorem, we show… (More)

- Gerd Grubb, H. Abels, J.-M. Bony, L. Boutet de Monvel, J. Brüning, N. Dencker +11 others
- 2008

- Gerd Grubb, Elmar Schrohe
- 2008

For a pseudodifferential boundary operator A of order ν ∈ Z and class 0 (in the Boutet de Monvel calculus) on a compact n-dimensional manifold with boundary, we consider the function Tr(AB −s), where B is an auxiliary system formed of the Dirichlet realization of a second order strongly elliptic differential operator and an elliptic operator on the… (More)

Let fT p : q 1 p q 2 g be a family of consistent C 0 semigroups on L p ((), with q 1 ; q 2 2 1; 1) and R n open. We show that certain commutator conditions on T p and on the resolvent of its generator A p ensure the p independence of the spectrum of A p for p 2 q 1 ; q 2 ]. Applications include the case of Petrovskij correct systems with HH older continuous… (More)