@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : I. The index of families of cone-degenerate operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26327},
  year      = {2002},
  abstract  = {We study the index problem for families of elliptic operators on manifolds with conical singularities. The relative index theorem concerning changes of the weight line is obtained. AN index theorem for families whose conormal symbols satisfy some symmetry conditions is derived.},
  language  = {en}
}
@unpublished{EgorovKondratievSchulze2001,
  author    = {Egorov, Yu. and Kondratiev, V. and Schulze, Bert-Wolfgang},
  title     = {On completeness of eigenfunctions of an elliptic operator on a manifold with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25937},
  year      = {2001},
  abstract  = {Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Completeness of root functions},
  language  = {en}
}
@unpublished{FladSchneiderSchulze2007,
  author    = {Flad, Heinz-J{\"u}rgen and Schneider, Reinhold and Schulze, Bert-Wolfgang},
  title     = {Asymptotic regularity of solutions of Hartree-Fock equations with coulomb potential},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30268},
  year      = {2007},
  abstract  = {We study the asymptotic regularity of solutions of Hartree-Fock equations for Coulomb systems. In order to deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo-differential operators on conical manifolds. First, the non-self-consistent-field case is considered which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator which guarantee ellipticity for the local part of the Fock operator on the open stretched cone R+ × S². This proves existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed-point approach based on Cances and Le Bris analysis of the level-shifting algorithm, we show via another bootstrap argument, that the corresponding self-consistent-field solutions of the Hartree-Fock equation have the same type of asymptotic regularity.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotics of solutions to elliptic equatons on manifolds with corners},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25716},
  year      = {2000},
  abstract  = {We show an explicit link between the nature of a singular point and behaviour of the coefficients of the equation, under which formal asymptotic expansions are still available.},
  language  = {en}
}
@unpublished{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Operator algebras with symbol hierarchies on manifolds with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25647},
  year      = {1999},
  abstract  = {Problems for elliptic partial differential equations on manifolds M with singularities M' (here with piece-wise smooth geometry)are studied in terms of pseudo-differential algebras with hierarchies of symbols that consist of scalar and operator-valued components. Classical boundary value problems (with or without the transmission property) belong to the examples. They are a model for operator algebras on manifolds M with higher "polyhedral" singularities. The operators are block matrices that have upper left corners containing the pseudo-differential operators on the regular M\M' (plus certain Mellin and Green summands) and are degenerate (in streched coordinates) in a typical way near M'. By definition M' is again a manifold with singularities. The same is true of M'', and so on. The block matrices consist of trace, potential and Mellin and Green operators, acting between weighted Sobolev spaces on M(j) and M(k), with 0 ≤ j, k ≤ ord M; here M(0) denotes M, M(1) denotes M', etc. We generate these algebras, including their symbol hierarchies, by iterating so-called "edgifications" and "conifications" os algebras that have already been constructed, and we study ellipicity, parametrics and Fredholm property within these algebras.},
  language  = {en}
}
@unpublished{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {An algebra of boundary value problems not requiring Shapiro-Lopatinskil conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25596},
  year      = {1999},
  abstract  = {We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro-Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices. Global pseudo-differential projections on the boundary are used to define ellipticity and to show the Fredholm property in suitable scales of spaces.},
  language  = {en}
}
@unpublished{KapanadzeSchulzeWitt2000,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang and Witt, Ingo},
  title     = {Coordinate invariance of the cone algebra with asymptotics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25671},
  year      = {2000},
  abstract  = {The cone algebra with discrete asymptotics on a manifold with conical singularities is shown to be invariant under natural coordinate changes, where the symbol structure (i.e., the Fuchsian interior symbol, conormal symbols of all orders) follows a corresponding transformation rule.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Part II: Quantization by the method of ordered operators (Noncommutative Analysis) : Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25762},
  year      = {2000},
  abstract  = {Content: 0.1 Preliminary Remarks Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems 1.1 Functions of One Operator (Functional Calculi) 1.2 Functions of Several Operators 1.3 Main Formulas of Operator Calculus 1.4 Main Tools of Noncommutative Analysis 1.5 Composition Laws and Ordered Representations},
  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{NazaikinskiiSchulzeSternin1999,
  author    = {Nazaikinskii, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25582},
  year      = {1999},
  abstract  = {In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.},
  language  = {en}
}
@unpublished{SavinSchulzeSternin2000,
  author    = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic operators in subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25701},
  year      = {2000},
  abstract  = {We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.},
  language  = {en}
}
@unpublished{SchulzeSterninSavin1999,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Savin, Anton},
  title     = {The homotopy classification and the index of boundary value problems for general elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25568},
  year      = {1999},
  abstract  = {We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.},
  language  = {en}
}
@unpublished{ManicciaSchulze2002,
  author    = {Maniccia, L. and Schulze, Bert-Wolfgang},
  title     = {An algebra of meromorphic corner symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26360},
  year      = {2002},
  abstract  = {Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.},
  language  = {en}
}
@unpublished{OliaroSchulze2002,
  author    = {Oliaro, Alessandro and Schulze, Bert-Wolfgang},
  title     = {Parameter-dependent boundary value problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26424},
  year      = {2002},
  abstract  = {As is known from Kondratyev's work, boundary value problems for elliptic operators on a manifold with conical singularities and boundary are controlled by a principal symbolic hierarchy, where the conormal symbols belong to the typical new components, compared with the smooth case, with interior and boundary symbols. A similar picture may be expected on manifolds with corners when the base of the cone itself is a manifold with conical or edge singularities. This is a natural situation in a number of applications, though with essential new difficulties. We investigate here corresponding conormal symbols in terms of a calculus of holomorphic parameter-dependent edge boundary value problems on the base. We show that a certain kernel cut-off procedure generates all such holomorphic families, modulo smoothing elements, and we establish conormal symbols as an algebra as is necessary for a parametrix constructions in the elliptic case.},
  language  = {en}
}
@unpublished{CoriascoSchulze2002,
  author    = {Coriasco, Sandro and Schulze, Bert-Wolfgang},
  title     = {Edge problems on configurations with model cones of different dimensions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26438},
  year      = {2002},
  abstract  = {Elliptic equations on configurations W = W1 ∪ ... ∪ Wn with edge Y and components Wj of different dimension can be treated in the frame of pseudo-differential analysis on manifolds with geometric singularities, here, edges. Starting from edge-degenerate operators on Wj, j = 1, ..., N, we construct an algebra with extra "transmission" conditions on Y that satisfy an analogue of the Shapiro-Lopatinskij condition. Ellipticity refers to a two-component symbolic hierarchy with an interior and an edge part; the latter one is operator-valued, operating on the union of different dimensional model cones. We construct parametrices within our calculus, where exchange of information between the various components is encoded in Green and Mellin operators that are smoothing on W\Y. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics.},
  language  = {en}
}
@unpublished{SchulzeSeiler2002,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Pseudodifferential boundary value problems with global projection conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26233},
  year      = {2002},
  abstract  = {Contents: Introduction 1 Operators with the transmission property 1.1 Operators on a manifold with boundary 1.2 Conditions with pseudodifferential projections 1.3 Projections and Fredholm families 2 Boundary value problems not requiring the transmission property 2.1 Interior operators 2.2 Edge amplitude functions 2.3 Boundary value problems 3 Operators with global projection conditions 3.1 Construction for boundary symbols 3.2 Ellipticity of boundary value problems with projection data 3.3 Operators of order zero},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2001,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Localization problem in index theory of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26175},
  year      = {2001},
  abstract  = {This is a survey of recent results concerning the general index locality principle, associated surgery, and their applications to elliptic operators on smooth manifolds and manifolds with singularities as well as boundary value problems. The full version of the paper is submitted for publication in Russian Mathematical Surveys.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : III. The spectral flow of families of conormal symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26386},
  year      = {2002},
  abstract  = {When studyind elliptic operators on manifolds with nonisolated singularities one naturally encounters families of conormal symbols (i.e. operators elliptic with parameter p ∈ IR in the sense of Agranovich-Vishik) parametrized by the set of singular points. For homotopies of such families we define the notion of spectral flow, which in this case is an element of the K-group of the parameter space. We prove that the spectral flow is equal to the index of some family of operators on the infinite cone.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2002,
  author    = {Harutjunjan, G. and Schulze, Bert-Wolfgang},
  title     = {Reduction of orders in boundary value problems without the transmission property},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26220},
  year      = {2002},
  abstract  = {Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We consider smooth symbols and ellipticity without additional boundary conditions which is the relevant case on a manifold with boundary. Starting from a class of symbols that has been investigated before for integer orders in boundary value problems with the transmission property we study operators of arbitrary real orders that play a similar role for operators without the transmission property. Moreover, we show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We finally investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary.},
  language  = {en}
}
@unpublished{NazaikinskiiSavinSchulzeetal.2002,
  author    = {Nazaikinskii, Vladimir and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic theory on manifolds with nonisolated singularities : IV. Obstructions to elliptic problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26415},
  year      = {2002},
  abstract  = {The obstruction to the existence of Fredholm problems for elliptic differentail operators on manifolds with edges is a topological invariant of the operator. We give an explicit general formula for this invariant. As an application we compute this obstruction for geometric operators.},
  language  = {en}
}