@unpublished{AbedSchulze2009,
  author    = {Abed, Jamil and Schulze, Bert-Wolfgang},
  title     = {Edge-degenerate families of ΨDO's on an infinite cylinder},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30365},
  year      = {2009},
  abstract  = {We establish a parameter-dependent pseudo-differential calculus on an infinite cylinder, regarded as a manifold with conical exits to infinity. The parameters are involved in edge-degenerate form, and we formulate the operators in terms of operator-valued amplitude functions.},
  language  = {en}
}
@unpublished{AbedSchulze2008,
  author    = {Abed, Jamil and Schulze, Bert-Wolfgang},
  title     = {Operators with corner-degenerate symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30299},
  year      = {2008},
  abstract  = {We establish elements of a new approch to ellipticity and parametrices within operator algebras on a manifold with higher singularities, only based on some general axiomatic requirements on parameter-dependent operators in suitable scales of spaces. The idea is to model an iterative process with new generations of parameter-dependent operator theories, together with new scales of spaces that satisfy analogous requirements as the original ones, now on a corresponding higher level. The "full" calculus is voluminous; so we content ourselves here with some typical aspects such as symbols in terms of order reducing families, classes of relevant examples, and operators near the conical exit to infinity.},
  language  = {en}
}
@unpublished{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25231},
  year      = {1998},
  abstract  = {Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.},
  language  = {en}
}
@unpublished{CalvoSchulze2005,
  author    = {Calvo, D. and Schulze, Bert-Wolfgang},
  title     = {Operators on corner manifolds with exit to infinity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29753},
  year      = {2005},
  abstract  = {We study (pseudo-)differential operators on a manifold with edge Z, locally modelled on a wedge with model cone that has itself a base manifold W with smooth edge Y . The typical operators A are corner degenerate in a specific way. They are described (modulo 'lower order terms') by a principal symbolic hierarchy σ(A) = (σ ψ(A), σ ^(A), σ ^(A)), where σ ψ is the interior symbol and σ ^(A)(y, η), (y, η) 2 T*Y \ 0, the (operator-valued) edge symbol of 'first generation', cf. [15]. The novelty here is the edge symbol σ^ of 'second generation', parametrised by (z, Ϛ) 2 T*Z \ 0, acting on weighted Sobolev spaces on the infinite cone with base W. Since such a cone has edges with exit to infinity, the calculus has the problem to understand the behaviour of operators on a manifold of that kind. We show the continuity of corner-degenerate operators in weighted edge Sobolev spaces, and we investigate the ellipticity of edge symbols of second generation. Starting from parameter-dependent elliptic families of edge operators of first generation, we obtain the Fredholm property of higher edge symbols on the corresponding singular infinite model cone.},
  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{DeDonnoSchulze2003,
  author    = {De Donno, G. and Schulze, Bert-Wolfgang},
  title     = {Meromorphic symbolic structures for boundary value problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26570},
  year      = {2003},
  abstract  = {We investigate the ideal of Green and Mellin operators with asymtotics for a manifold with edge-corner singularities and boundary which belongs to the structure of parametrices of elliptic boundary value problems on a configuration with corners whose base manifolds have edges.},
  language  = {en}
}
@unpublished{DinesHarutjunjanSchulze2003,
  author    = {Dines, Nicoleta and Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem in edge Sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26615},
  year      = {2003},
  abstract  = {Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.},
  language  = {en}
}
@unpublished{DinesLiuSchulze2004,
  author    = {Dines, Nicoleta and Liu, X. and Schulze, Bert-Wolfgang},
  title     = {Edge quantisation of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26838},
  year      = {2004},
  abstract  = {The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.},
  language  = {en}
}
@unpublished{DinesSchulze2003,
  author    = {Dines, Nicoleta and Schulze, Bert-Wolfgang},
  title     = {Mellin-edge representations of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26627},
  year      = {2003},
  abstract  = {We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P.},
  language  = {en}
}
@unpublished{EgorovKondratievSchulze2004,
  author    = {Egorov, Jurij V. and Kondratiev, V. A. and Schulze, Bert-Wolfgang},
  title     = {On the completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26773},
  year      = {2004},
  abstract  = {Contents: 1 Introduction 2 Definitions 3 Rays of minimal growth 4 Proof of Theorem 2. 5 The growth of the resolvent 6 Proof of Theorem 3. 7 The completeness of root functions 8 Some generalizations},
  language  = {en}
}