@unpublished{LauterSeiler1999,
  author    = {Lauter, Robert and Seiler, J{\"o}rg},
  title     = {Pseudodifferential analysis on manifolds with boundary - a comparison of b-calculus and cone algebra},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25611},
  year      = {1999},
  abstract  = {We establish a relation between two different approaches to a complete pseudodifferential analysis of totally characteristic or Fuchs type operators on compact manifolds with boundary respectively conical singularities: Melrose's (overblown) b-calculus and Schulze's cone algebra. Though quite different in their definition, we show that these two pseudodifferential calculi basically contain the same operators.},
  language  = {en}
}
@unpublished{KytmanovMyslivetsTarkhanov1999,
  author    = {Kytmanov, Alexander and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Analytic representation of CR Functions on hypersurfaces with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25631},
  year      = {1999},
  abstract  = {We prove a theorem on analytic representation of integrable CR functions on hypersurfaces with singular points. Moreover, the behaviour of representing analytic functions near singular points is investigated. We are aimed at explaining the new effect caused by the presence of a singularity rather than at treating the problem in full generality.},
  language  = {en}
}
@unpublished{BoeckmannSarkoezi1999,
  author    = {B{\"o}ckmann, Christine and Sark{\"o}zi, Janos},
  title     = {The ill-posed inversion of multiwavelength lidar data by a hybrid method of variable projection},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14847},
  year      = {1999},
  abstract  = {The ill-posed problem of aerosol distribution determination from a small number of backscatter and extinction lidar measurements was solved successfully via a hybrid method by a variable dimension of projection with B-Splines. Numerical simulation results with noisy data at different measurement situations show that it is possible to derive a reconstruction of the aerosol distribution only with 4 measurements.},
  language  = {en}
}
@unpublished{SchroheSeiler1999,
  author    = {Schrohe, Elmar and Seiler, J{\"o}rg},
  title     = {Ellipticity and invertibility in the cone algebra on Lp-Sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25621},
  year      = {1999},
  abstract  = {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 inversion: whenever an operator is invertible between the associated Sobolev spaces, its inverse belongs to the calculus. We use these results to analyze the behaviour of these operators on Lp(B).},
  language  = {en}
}
@unpublished{Fedosov1999,
  author    = {Fedosov, Boris},
  title     = {Pseudo-differential operators and deformation quantization},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25651},
  year      = {1999},
  abstract  = {Using the Riemannian connection on a compact manifold X, we show that the algebra of classical pseudo-differential operators on X generates a canonical deformation quantization on the cotangent manifold T*X. The corresponding Abelian connection is calculated explicitly in terms of the of the exponential mapping. We prove also that the index theorem for elliptic operators may be obtained as a consequence of the index theorem for deformation quantization.},
  language  = {en}
}
@unpublished{Sadykov1999,
  author    = {Sadykov, Timour},
  title     = {Hypergeometric systems of differential equations and amoebas of rational functions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25665},
  year      = {1999},
  abstract  = {We study the approach to the theory of hypergeometric functions in several variables via a generalization of the Horn system of differential equations. A formula for the dimension of its solution space is given. Using this formula we construct an explicit basis in the space of holomorphic solutions to the generalized Horn system under some assumptions on its parameters. These results are applied to the problem of describing the complement of the amoeba of a rational function, which was posed in [12].},
  language  = {en}
}
@unpublished{Schrohe1999,
  author    = {Schrohe, Elmar},
  title     = {Noncommutative residues, Dixmier's Trace, and heat trace expansions on manifolds with boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25486},
  year      = {1999},
  abstract  = {For manifolds with boundary, we define an extension of Wodzicki's noncommutative residue to boundary value problems in Boutet de Monvel's calculus. We show that this residue can be recovered with the help of heat kernel expansions and explore its relation to Dixmier's trace.},
  language  = {en}
}
@unpublished{NazaikinskiiSternin1999,
  author    = {Nazaikinskii, Vladimir E. and Sternin, Boris},
  title     = {Surgery and the relative index in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25538},
  year      = {1999},
  abstract  = {We prove a general theorem on the local property of the relative index for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions) this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities as well as for elliptic boundary value problems with a symmetry condition for the conormal symbol.},
  language  = {en}
}
@unpublished{SavinSternin1999,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Elliptic operators in even subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25461},
  year      = {1999},
  abstract  = {An elliptic theory is constructed for operators acting in subspaces defined via even pseudodifferential projections. Index formulas are obtained for operators on compact manifolds without boundary and for general boundary value problems. A connection with Gilkey's theory of η-invariants is established.},
  language  = {en}
}
@unpublished{Witt1999,
  author    = {Witt, Ingo},
  title     = {On the factorization of meromorphic Mellin symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25427},
  year      = {1999},
  abstract  = {It is prooved that mermorphic, parameter-dependet elliptic Mellin symbols can be factorized in a particular way. The proof depends on the availability of logarithms of pseudodifferential operators. As a byproduct, we obtain a characterization of the group generated by pseudodifferential operators admitting a logarithm. The factorization has applications to the theory os pseudodifferential operators on spaces with conical singularities, e.g., to the index theory and the construction of various sub-calculi of the cone calculus.},
  language  = {en}
}