@article{ChangSchulze2018,
  author    = {Chang, Der-Chen and Schulze, Bert-Wolfgang},
  title     = {Corner spaces and Mellin quantization},
  series = {Journal of nonlinear and convex analysis : an international journal},
  volume    = {19},
  journal   = {Journal of nonlinear and convex analysis : an international journal},
  number    = {2},
  publisher = {Yokohama Publishers},
  address   = {Yokohama},
  issn      = {1345-4773},
  pages     = {179 -- 195},
  year      = {2018},
  abstract  = {Manifolds with corners in the present investigation are non-smooth configurations - specific stratified spaces - with an incomplete metric such as cones, manifolds with edges, or corners of piecewise smooth domains in Euclidean space. We focus here on operators on such "corner manifolds" of singularity order <= 2, acting in weighted corner Sobolev spaces. The corresponding corner degenerate pseudo-differential operators are formulated via Mellin quantizations, and they also make sense on infinite singular cones.},
  language  = {en}
}
@book{CoriascoSchulze2002,
  author    = {Coriasco, S. and Schulze, Bert-Wolfgang},
  title     = {Edge Problems on Configurations with Model Cones of Different Dimensions},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {41 S.},
  year      = {2002},
  language  = {en}
}
@article{CoriascoSchulze2006,
  author    = {Coriasco, Sandro and Schulze, Bert-Wolfgang},
  title     = {Edge problems on configurations with model cones of different dimensions},
  issn      = {0030-6126},
  year      = {2006},
  abstract  = {Elliptic equations on configurations W = W-1 boolean OR (. . .) boolean OR W-N with edge Y and components W-j 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 WY. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics},
  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}
}
@book{DeDonnoSchulze2003,
  author    = {De Donno, G. and Schulze, Bert-Wolfgang},
  title     = {Meromorphic symbolic structures for boundary value problems on manifolds with edges},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {40 S.},
  year      = {2003},
  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}
}
@article{DeDonnoSchulze2006,
  author    = {De Donno, Giuseppe and Schulze, Bert-Wolfgang},
  title     = {Meromorphic symbolic structures for boundary value problems on manifolds with edges},
  issn      = {0025-584X},
  doi       = {10.1002/mana.200310366},
  year      = {2006},
  abstract  = {We investigate the ideal of Green and Mellin operators with asymptotics 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}
}
@book{DinesHarutjunjanSchulze2003,
  author    = {Dines, Nicoleta and Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem in edge sobolev spaces},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {38 S.},
  year      = {2003},
  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}
}
@article{DinesLiuSchulze2009,
  author    = {Dines, Nicoleta and Liu, Xiaochun and Schulze, Bert-Wolfgang},
  title     = {Edge quantisation of elliptic operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  issn      = {1437-739X},
  doi       = {10.1007/s00605-008-0058-y},
  year      = {2009},
  abstract  = {The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy sigma = (sigma(psi), sigma(boolean AND)), where the second component takes values in operators on the infinite model cone of the local wedges. In the general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the ellipticity of the principal edge symbol sigma(boolean AND) which includes the (in general not explicity known) number of additional conditions of trace and potential type on the edge. We focus here on these questions 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.},
  language  = {en}
}
@article{DinesSchulze2005,
  author    = {Dines, Nicoleta and Schulze, Bert-Wolfgang},
  title     = {Mellin-edge representations of elliptic operators},
  issn      = {0170-4214},
  year      = {2005},
  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 A(s) in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of A(s) as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices P-s of A(s) interpreted as Mellin-edge representations of P. Copyright (c) 2005 John Wiley \& Sons, Ltd},
  language  = {en}
}
@book{DinesSchulze2003,
  author    = {Dines, Nicoleta and Schulze, Bert-Wolfgang},
  title     = {Melin-edges representations of elliptic operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {43 S.},
  year      = {2003},
  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}
}
@article{DorschfeldtGriemeSchulze1997,
  author    = {Dorschfeldt, Christoph and Grieme, Ulrich and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential calculus in the Fourieredge approach on non-compact manifolds},
  year      = {1997},
  language  = {en}
}
@article{DorschfeldtSchulze1994,
  author    = {Dorschfeldt, Christoph and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential operators with operator-valued symbols in the Mellin-edge-approach},
  year      = {1994},
  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}
}
@book{EgorovSchulze1997,
  author    = {Egorov, Jurij V. and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential operators, singularities, applicatons},
  series = {Operator theory},
  volume    = {93},
  journal   = {Operator theory},
  publisher = {Birkh{\"a}user},
  address   = {Basel},
  isbn      = {3-7643-5484-4},
  pages     = {XII; 349 S.},
  year      = {1997},
  language  = {en}
}
@book{EgorovKondratievSchulze2001,
  author    = {Egorov, Yu and Kondratiev, V. A. and Schulze, Bert-Wolfgang},
  title     = {On completeness of eigenfunctions of an elliptic operator on a manifold with concial points},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgrupe Partielle Differentialgleichun},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgrupe Partielle Differentialgleichun},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-339X},
  pages     = {11 S.},
  year      = {2001},
  language  = {en}
}
@book{EgorovKondratievSchulze2004,
  author    = {Egorov, Yu. 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},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {21 S.},
  year      = {2004},
  language  = {en}
}