@unpublished{AirapetyanWitt1997,
  author    = {Airapetyan, Ruben and Witt, Ingo},
  title     = {Isometric properties of the Hankel Transformation in weighted sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25001},
  year      = {1997},
  abstract  = {It is shown that the Hankel transformation Hsub(v) acts in a class of weighted Sobolev spaces. Especially, the isometric mapping property of Hsub(v) which holds on L²(IRsub(+),rdr) is extended to spaces of arbitrary Sobolev order. The novelty in the approach consists in using techniques developed by B.-W. Schulze and others to treat the half-line Rsub(+) as a manifold with a conical singularity at r = 0. This is achieved by pointing out a connection between the Hankel transformation and the Mellin transformation.The procedure proposed leads at the same time to a short proof of the Hankel inversion formula. An application to the existence and higher regularity of solutions, including their asymptotics, to the 1-1-dimensional edge-degenerated wave equation is given.},
  language  = {en}
}
@unpublished{BoeckmannBieleNeuberetal.1997,
  author    = {B{\"o}ckmann, Christine and Biele, Jens and Neuber, Roland and Niebsch, Jenny},
  title     = {Retrieval of multimodal aerosol size distribution by inversion of multiwavelength data},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-14360},
  year      = {1997},
  abstract  = {The ill-posed problem of aerosol size distribution determination from a small number of backscatter and extinction measurements was solved successfully with a mollifier method which is advantageous since the ill-posed part is performed on exactly given quantities, the points r where n(r) is evaluated may be freely selected. A new twodimensional model for the troposphere is proposed.},
  language  = {en}
}
@unpublished{GalstianYagdjian1997,
  author    = {Galstian, Anahit and Yagdjian, Karen},
  title     = {Exponential function of pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24982},
  year      = {1997},
  abstract  = {The paper is devoted to the construction of the exponential function of a matrix pseudo-differential operator which do not satisfy any of the known theorems (see, Sec.8 Ch.VIII and Sec.2 Ch.XI of [17]). The applications to the construction of the fundamental solution for the Cauchy problem for the hyperbolic operators with the characteristics of variable multiplicity are given, too.},
  language  = {en}
}
@unpublished{Fedosov1997,
  author    = {Fedosov, Boris},
  title     = {Non-Abelian reduction in deformation quantization},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25101},
  year      = {1997},
  abstract  = {We consider a G-invariant star-product algebra A on a symplectic manifold (M,ω) obtained by a canonical construction of deformation quantization. Under assumptions of the classical Marsden-Weinstein theorem we define a reduction of the algebra A with respect to the G-action. The reduced algebra turns out to be isomorphic to a canonical star-product algebra on the reduced phase space B. In other words, we show that the reduction commutes with the canonical G-invariant deformation quantization. A similar statement in the framework of geometric quantization is known as the Guillemin-Sternberg conjecture (by now completely proved).},
  language  = {en}
}
@unpublished{HieberSchrohe1997,
  author    = {Hieber, Matthias and Schrohe, Elmar},
  title     = {Lρ spectral independence of elliptic operators via commutator estimates},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25047},
  year      = {1997},
  abstract  = {Let {Tsub(p) : q1 ≤ p ≤ q2} be a family of consistent Csub(0) semigroups on Lφ(Ω) with q1, q2 ∈ [1, ∞)and Ω ⊆ IRn open. We show that certain commutator conditions on Tφ and on the resolvent of its generator Aφ ensure the φ independence of the spectrum of Aφ for φ ∈ [q1, q2]. Applications include the case of Petrovskij correct systems with H{\"o}lder continuous coeffcients, Schr{\"o}dinger operators, and certain elliptic operators in divergence form with real, but not necessarily symmetric, or complex coeffcients.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The Riemann-Roch theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25051},
  year      = {1997},
  abstract  = {The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Operator algebras on singular manifolds. I},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25011},
  year      = {1997},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {On the index of differential operators on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24965},
  year      = {1997},
  abstract  = {The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Nonstationary problems for equations of Borel-Fuchs type},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24973},
  year      = {1997},
  abstract  = {In the paper, the nonstationary problems for equations of Borel-Fuchs type are investigated. The asymptotic expansion are obtained for different orders of degeneration of operators in question. The approach to nonstationary problems based on the asymptotic theory on abstract algebras is worked out.},
  language  = {en}
}
@unpublished{RabinovichSchulzeTarkhanov1997,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A calculus of boundary value problems in domains with Non-Lipschitz Singular Points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24957},
  year      = {1997},
  abstract  = {The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Lefschetz theory on manifolds with edges : introduction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24948},
  year      = {1997},
  abstract  = {The aim of this book is to develop the Lefschetz fixed point theory for elliptic complexes of pseudodifferential operators on manifolds with edges. The general Lefschetz theory contains the index theory as a special case, while the case to be studied is much more easier than the index problem. The main topics are: - The calculus of pseudodifferential operators on manifolds with edges, especially symbol structures (inner as well as edge symbols). - The concept of ellipticity, parametrix constructions, elliptic regularity in Sobolev spaces. - Hodge theory for elliptic complexes of pseudodifferential operators on manifolds with edges. - Development of the algebraic constructions for these complexes, such as homotopy, tensor products, duality. - A generalization of the fixed point formula of Atiyah and Bott for the case of simple fixed points. - Development of the fixed point formula also in the case of non-simple fixed points, provided that the complex consists of diferential operarators only. - Investigation of geometric complexes (such as, for instance, the de Rham complex and the Dolbeault complex). Results in this direction are desirable because of both purely mathe matical reasons and applications in natural sciences.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1997,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The index of elliptic operators on manifolds with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25096},
  year      = {1997},
  abstract  = {For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Operator algebras on singular manifolds. IV, V},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25062},
  year      = {1997},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {A Lefschetz fixed point theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25073},
  year      = {1997},
  abstract  = {We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {On general boundary value problems for elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25138},
  year      = {1997},
  abstract  = {We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSterninetal.1997,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris and Shatalov, Victor},
  title     = {Spectral boundary value problems and elliptic equations on singular manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25147},
  year      = {1997},
  abstract  = {For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Quantization of symplectic transformations on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25084},
  year      = {1997},
  abstract  = {The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1997,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On the index formula for singular surfaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25116},
  year      = {1997},
  abstract  = {In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators.},
  language  = {en}
}
@unpublished{Korkey1998,
  author    = {Korkey, Michael Brian},
  title     = {Optimal factorization of Muckenhoupt weights},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25266},
  year      = {1998},
  abstract  = {Peter Jones' theorem on the factorization of Ap weights is sharpened for weights with bounds near 1, allowing the factorization to be performed continuously near the limiting, unweighted case. When 1 < p < infinite and omega is an Ap weight with bound Ap(omega) = 1 + epsilon, it is shown that there exist Asub1 weights u, v such that both the formula omega = uv(1-p) and the estimates A1 (u), A1 (v) = 1 + Omikron (√epsilon) hold. The square root in these estimates is also proven to be the correct asymptotic power as epsilon -> 0.},
  language  = {en}
}
@unpublished{ChenHidetoshi1998,
  author    = {Chen, Hua and Hidetoshi, Tahara},
  title     = {On the holomorphic solution of non-linear totally characteristic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25333},
  year      = {1998},
  abstract  = {The paper deals with a non-linear singular partial differential equation: (E) t∂/∂t = F(t, x, u, ∂u/∂x) in the holomorphic category. When (E) is of Fuchsian type, the existence of the unique holomorphic solution was established by G{\´e}rard-Tahara [2]. In this paper, under the assumption that (E) is of totally characteristic type, the authors give a sufficient condition for (E) to have a unique holomorphic solution. The result is extended to higher order case.},
  language  = {en}
}