@unpublished{SchulzeTarkhanov1997,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@unpublished{RabinovichSchulzeTarkhanov1997,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@unpublished{SchulzeTarkhanov1997,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{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{RabinovichSchulzeTarkhanov1998,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems in cuspidal wedges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25363},
  year      = {1998},
  abstract  = {The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. Concerning the geometry we even admit a more general behaviour, namely oscillating cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Elliptic complexes of pseudodifferential operators on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25257},
  year      = {1998},
  abstract  = {On a compact closed manifold with edges live pseudodifferential operators which are block matrices of operators with additional edge conditions like boundary conditions in boundary value problems. They include Green, trace and potential operators along the edges, act in a kind of Sobolev spaces and form an algebra with a wealthy symbolic structure. We consider complexes of Fr{\´e}chet spaces whose differentials are given by operators in this algebra. Since the algebra in question is a microlocalization of the Lie algebra of typical vector fields on a manifold with edges, such complexes are of great geometric interest. In particular, the de Rham and Dolbeault complexes on manifolds with edges fit into this framework. To each complex there correspond two sequences of symbols, one of the two controls the interior ellipticity while the other sequence controls the ellipticity at the edges. The elliptic complexes prove to be Fredholm, i.e., have a finite-dimensional cohomology. Using specific tools in the algebra of pseudodifferential operators we develop a Hodge theory for elliptic complexes and outline a few applications thereof.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Euler solutions of pseudodifferential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25211},
  year      = {1998},
  abstract  = {We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.},
  language  = {en}
}
@unpublished{NacinovichSchulzeTarkhanov1998,
  author    = {Nacinovich, Mauro and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On carleman formulas for the dolbeault cohomology},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25224},
  year      = {1998},
  abstract  = {We discuss the Cauchy problem for the Dolbeault cohomology in a domain of C n with data on a part of the boundary. In this setting we introduce the concept of a Carleman function which proves useful in the study of uniqueness. Apart from an abstract framework we show explicit Carleman formulas for the Dolbeault cohomology.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1998,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A remark on the index of symmetric operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169},
  year      = {1998},
  abstract  = {We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Lefschetz fixed point formula in the relative elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25159},
  year      = {1998},
  abstract  = {A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1998,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The index of higher order operators on singular surfaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25127},
  year      = {1998},
  abstract  = {The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.},
  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{AizenbergTarkhanov1999,
  author    = {Aizenberg, Lev A. and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Bohr phenomenon for elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25547},
  year      = {1999},
  abstract  = {In 1914 Bohr proved that there is an r ∈ (0, 1) such that if a power series converges in the unit disk and its sum has modulus less than 1 then, for |z| < r, the sum of absolute values of its terms is again less than 1. Recently analogous results were obtained for functions of several variables. The aim of this paper is to comprehend the theorem of Bohr in the context of solutions to second order elliptic equations meeting the maximum principle.},
  language  = {en}
}
@unpublished{SchulzeShlapunovTarkhanov1999,
  author    = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Regularisation of mixed boundary problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25454},
  year      = {1999},
  abstract  = {We show an application of the spectral theorem in constructing approximate solutions of mixed boundary value problems for elliptic equations.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1999,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A general index formula on tropic manifolds with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25501},
  year      = {1999},
  abstract  = {We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1999,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Ellipticity and parametrices on manifolds with caspidal edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25411},
  year      = {1999},
  language  = {en}
}
@unpublished{RabinovichSchulzeTarkhanov1999,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems in domains with corners},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25552},
  year      = {1999},
  abstract  = {We describe Fredholm boundary value problems for differential equations in domains with intersecting cuspidal edges on the boundary.},
  language  = {en}
}
@unpublished{KytmanovMyslivetsTarkhanov2000,
  author    = {Kytmanov, Aleksandr and Myslivets, Simona and Tarkhanov, Nikolai Nikolaevich},
  title     = {Removable singularities of CR functions on singular boundaries},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25836},
  year      = {2000},
  abstract  = {The problem of analytic representation of integrable CR functions on hypersurfaces with singularities is treated. The nature o singularities does not matter while the set of singularities has surface measure zero. For simple singularities like cuspidal points, edges, corners, etc., also the behaviour of representing analytic functions near singular points is studied.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Pseudodifferential operators on manifolds with corners},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25783},
  year      = {2000},
  abstract  = {We describe an algebra of pseudodifferential operators on a manifold with corners.},
  language  = {en}
}