@unpublished{DenkKrainer2006,
  author    = {Denk, Robert and Krainer, Thomas},
  title     = {R-Boundedness, pseudodifferential operators, and maximal regularity for some classes of partial differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30147},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@unpublished{GilKrainerMendoza2004,
  author    = {Gil, Juan B. and Krainer, Thomas and Mendoza, Gerardo A.},
  title     = {Geometry and spectra of closed extensions of elliptic cone operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26815},
  year      = {2004},
  abstract  = {We study the geometry of the set of closed extensions of index 0 of an elliptic cone operator and its model operator in connection with the spectra of the extensions, and give a necessary and sufficient condition for the existence of rays of minimal growth for such operators.},
  language  = {en}
}
@unpublished{GilKrainerMendoza2004,
  author    = {Gil, Juan B. and Krainer, Thomas and Mendoza, Gerardo A.},
  title     = {Resolvents of elliptic cone operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26820},
  year      = {2004},
  abstract  = {We prove the existence of sectors of minimal growth for general closed extensions of elliptic cone operators under natural ellipticity conditions. This is achieved by the construction of a suitable parametrix and reduction to the boundary. Special attention is devoted to the clarification of the analytic structure of the resolvent.},
  language  = {en}
}
@unpublished{GilKrainerMendoza2006,
  author    = {Gil, Juan B. and Krainer, Thomas and Mendoza, Gerardo A.},
  title     = {On rays of minimal growth for elliptic cone operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30064},
  year      = {2006},
  abstract  = {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.},
  language  = {en}
}
@unpublished{Krainer2001,
  author    = {Krainer, Thomas},
  title     = {The calculus of Volterra Mellin pseudodifferential operators with operator-valued symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26185},
  year      = {2001},
  abstract  = {We introduce the calculus of Mellin pseudodifferential operators parameters based on "twisted" operator-valued Volterra symbols as well aas the abstract Mellin calclus with holomorphic symbols. We establish the properties of the symblic and operational calculi, and we give and make use of explicit oscillatory integral formulas on the symbolic side, e. g., for the Leibniz-product, kernel cut-off, and Mellin quantization. Moreover, we introduce the notion of parabolicity for the calculi of Volterra Mellin operators, and construct Volterra parametrices for parabolic operators within the calculi.},
  language  = {en}
}
@unpublished{Krainer2002,
  author    = {Krainer, Thomas},
  title     = {On the inverse of parabolic boundary value problems for large times},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26310},
  year      = {2002},
  abstract  = {We construct algebras of Volterra pseudodifferential operators that contain, in particular, the inverses of the most natural classical systems of parabolic boundary value problems of general form. Parabolicity is determined by the invertibility of the principal symbols, and as a result is equivalent to the invertibility of the operators within the calculus. Existence, uniqueness, regularity, and asymptotics of solutions as t → ∞ are consquences of the mapping properties of the operators in exponentially weighted Sobolev spaces and subspaces with asymptotics. An important aspect of this work is that the microlocal and global kernel structure of the inverse operator (solution operator) of a parabolic boundary value problem for large times is clarified. Moreover, our approach naturally yields qualitative pertubation results for the solvability theory of parabolic boundary value problems. To achieve these results, we assign t = ∞ the meaning of a conical point and treat the operators as totally characteristic pseudodifferential boundary value problems.},
  language  = {en}
}
@unpublished{Krainer2005,
  author    = {Krainer, Thomas},
  title     = {Elliptic boundary problems on manifolds with polycylindrical ends},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29912},
  year      = {2005},
  abstract  = {We investigate general Shapiro-Lopatinsky elliptic boundary value problems on manifolds with polycylindrical ends. This is accomplished by compactifying such a manifold to a manifold with corners of in general higher codimension, and we then deal with boundary value problems for cusp differential operators. We introduce an adapted Boutet de Monvel's calculus of pseudodifferential boundary value problems, and construct parametrices for elliptic cusp operators within this calculus. Fredholm solvability and elliptic regularity up to the boundary and up to infinity for boundary value problems on manifolds with polycylindrical ends follows.},
  language  = {en}
}
@unpublished{Krainer2005,
  author    = {Krainer, Thomas},
  title     = {Resolvents of elliptic boundary problems on conic manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29773},
  year      = {2005},
  abstract  = {We prove the existence of sectors of minimal growth for realizations of boundary value problems on conic manifolds under natural ellipticity conditions. Special attention is devoted to the clarification of the analytic structure of the resolvent.},
  language  = {en}
}
@unpublished{Krainer2002,
  author    = {Krainer, Thomas},
  title     = {On the calculus of pseudodifferential operators with an anisotropic analytic parameter},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26200},
  year      = {2002},
  abstract  = {We introduce the Volterra calculus of pseudodifferential operators with an anisotropic analytic parameter based on "twisted" operator-valued Volterra symbols. We establish the properties of the symbolic and operational calculi, and we give and make use of explicit oscillatory integral formulas on the symbolic side. In particular, we investigate the kernel cut-off operator via direct oscillatory integral techniques purely on symbolic level. We discuss the notion of parabolic for the calculus of Volterra operators, and construct Volterra parametrices for parabolic operators within the calculus.},
  language  = {en}
}
@unpublished{KrainerSchulze2000,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {Long-time asymptotics with geometric singularities in the spatial variables},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25824},
  year      = {2000},
  abstract  = {Content: Introduction 1 Anisotropic operators in a cylinder with a conical base 1.1 Manifolds with conical singularities and opertors of Fuchs type 1.2 Typical operators and symbol structures 2 Weighted wedge Sobolev spaces and edge asymptotics 2.1 Discrete edge asymptotics 2.2 Continuos edge asymptotics with discrete limit at infinity 2.3 Calculus with operator valued symbols 3 Corner asymptotics at infinity 3.1 The structure of singular functions 3.2 Operators with trace and potential conditions 3.3 Asymptotics and (anisotropic) elliptic regularity},
  language  = {en}
}