TY  - INPR
A1  - Gil, Juan B.
A1  - Krainer, Thomas
A1  - Mendoza, Gerardo A.
T1  - On rays of minimal growth for elliptic cone operators
N2  - We present an overview of some of our recent results on the existence of rays of minimal growth for elliptic cone operators and two new results concerning the necessity of certain conditions for the existence of such rays.
T3  - Preprint - (2006) 02 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30064
ER  - 
TY  - INPR
A1  - Denk, Robert
A1  - Krainer, Thomas
T1  - R-Boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators
N2  - It is shown that an elliptic scattering operator A on a compact manifold with boundary with operator valued coefficients in the morphisms of a bundle of Banach spaces of class (HT ) and Pisier’s property (α) has maximal regularity (up to a spectral shift), provided that the spectrum of the principal symbol of A on the scattering cotangent bundle avoids the right half-plane. This is accomplished by representing the resolvent in terms of pseudodifferential operators with R-bounded symbols, yielding by an iteration argument the R-boundedness of λ(A − λ)−1 in R(λ)≥ τ for some τ ∈ IR. To this end, elements of a symbolic and operator calculus of pseudodifferential operators with R-bounded symbols are introduced. The significance of this method for proving maximal regularity results for partial differential operators is underscored by considering also a more elementary situation of anisotropic elliptic operators on Rd with operator valued coefficients.
T3  - Preprint - (2006) 14 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30147
ER  -