TY  - INPR
A1  - Junker, Wolfgang
A1  - Schrohe, Elmar
T1  - Adiabatic vacuum states on general spacetime manifolds : definition, construction, and physical properties
N2  - Adiabatic vacuum states are a well-known class of physical states for linear quantum fields n 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 the adiabatic vacua. We analyze physical properties of adiabatic vacuum representations of the Klein-Gordon field on globally hyperbolic spacetme manifolds (factoriality, quasiequivalence, local definteness, Haag duality) and construct them explicitly, if the manifold has a compact Cauchy surface.
T3  - Preprint - (2001) 27 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26100
ER  - 
TY  - INPR
A1  - Coriasco, Sandro
A1  - Schrohe, Elmar
A1  - Seiler, Jörg
T1  - Bounded imaginary powers of differential operators on manifolds with conical singularities
N2  - 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 < ∞. Under suitable ellipticity assumptions we can define a family of complex powers A up(z), z ∈ C. We also obtain sufficient information on the resolvent of A to show the boundedness of the pure imaginary powers. Examples concern unique solvability and maximal regularity of the solution of the Cauchy problem u' - Δu = f, u(0) = 0, for the Laplacian on conical manifolds.
T3  - Preprint - (2001) 12 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25962
ER  - 
TY  - INPR
A1  - Melo, S. T.
A1  - Nest, R.
A1  - Schrohe, Elmar
T1  - C*-structure and K-theory of Boutet de Monvel's algebra
N2  - 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 topologically determined. In case the manifold, its boundary, and the cotangent space of its interior have torsion free K-theory, we get Ki(A,k) congruent Ki(C(X))⊕Ksub(1-i)(Csub(0)(T*X)),i = 0,1, with k denoting the compact ideal, and T*X denoting the cotangent bundle of the interior. Using Boutet de Monvel's index theorem, we also prove that the above formula holds for i = 1 even without this torsion-free hypothesis. For the case of orientable, two-dimensional X, Ksub(0)(A) congruent Z up(2g+m) and Ksub(1)(A) congruent Z up(2g+m-1), where g is the genus of X and m is the number of connected components of ∂X. We also obtain a composition sequence 0 ⊂ k ⊂ G ⊂ A, with A/G commutative and G/k isomorphic to the algebra of all continuous functions on the cosphere bundle of ∂X with values in compact operators on L²(R+).
T3  - Preprint - (2001) 33 
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26166
ER  -