@book{AbedSchulze2008,
  author    = {Abed, Jamil and Schulze, Bert-Wolfgang},
  title     = {Operators with Corner-degenerate Symbols},
  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     = {47 S.},
  year      = {2008},
  language  = {en}
}
@book{AlbeverioDemuthSchroheetal.2002,
  author    = {Albeverio, Sergio and Demuth, Michael and Schrohe, Elmar and Schulze, Bert-Wolfgang},
  title     = {Parabolicity, volterra calculus, and conical singularities : a volume of advances in partial differential equations},
  series = {Operator theory : advances and applications},
  volume    = {138},
  journal   = {Operator theory : advances and applications},
  publisher = {Birkh{\"a}user Verl.},
  address   = {Basel},
  isbn      = {3-7643-6906-x},
  pages     = {358 S.},
  year      = {2002},
  language  = {en}
}
@article{BuchholzSchulze1997,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Anisotropic edges pseudo-differential operators withdiscrete asymptotics},
  year      = {1997},
  language  = {en}
}
@book{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 11},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {57 S.},
  year      = {1998},
  language  = {en}
}
@article{BurenkovSchulzeTarchanov1998,
  author    = {Burenkov, V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Extension operators for sobolev spaces commuting with a given transform},
  year      = {1998},
  language  = {en}
}
@book{CalvoMartinSchulze2004,
  author    = {Calvo, D. and Martin, Calin-Iulian and Schulze, Bert-Wolfgang},
  title     = {Symbolic Structures on Corner Manifolds},
  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     = {18 S.},
  year      = {2004},
  language  = {en}
}
@book{CalvoSchulze2005,
  author    = {Calvo, D. and Schulze, Bert-Wolfgang},
  title     = {Operators on Corner Manifolds with Exit to Infinity},
  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     = {48 S.},
  year      = {2005},
  language  = {en}
}
@article{ChangSchulze2017,
  author    = {Chang, D. -C. and Schulze, Bert-Wolfgang},
  title     = {Calculus on spaces with higher singularities},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {8},
  journal   = {Journal of pseudo-differential operators and applications},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-016-0180-x},
  pages     = {585 -- 622},
  year      = {2017},
  abstract  = {We establish extensions of the standard pseudo-differential calculus to specific classes of operators with operator-valued symbols occurring in symbolic hierarchies motivated by manifolds with higher singularities or stratified spaces.},
  language  = {en}
}
@article{ChangViahmoudiSchulze2016,
  author    = {Chang, D. -C. and Viahmoudi, M. Hedayat and Schulze, Bert-Wolfgang},
  title     = {PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE},
  series = {Journal of nonlinear and convex analysis : an international journal},
  volume    = {17},
  journal   = {Journal of nonlinear and convex analysis : an international journal},
  publisher = {Yokohama Publishers},
  address   = {Yokohama},
  issn      = {1345-4773},
  pages     = {1889 -- 1937},
  year      = {2016},
  abstract  = {This paper is devoted to pseudo-differential operators and new applications. We establish necessary extensions of the standard calculus to specific classes of operator-valued symbols occurring in principal symbolic hierarchies of operators on manifolds with singularities or stratified spaces.},
  language  = {en}
}
@article{ChangHabalSchulze2014,
  author    = {Chang, Der-Chen and Habal, Nadia and Schulze, Bert-Wolfgang},
  title     = {The edge algebra structure of the Zaremba problem},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {5},
  journal   = {Journal of pseudo-differential operators and applications},
  number    = {1},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-013-0088-7},
  pages     = {69 -- 155},
  year      = {2014},
  abstract  = {We study mixed boundary value problems, here mainly of Zaremba type for the Laplacian within an edge algebra of boundary value problems. The edge here is the interface of the jump from the Dirichlet to the Neumann condition. In contrast to earlier descriptions of mixed problems within such an edge calculus, cf. (Harutjunjan and Schulze, Elliptic mixed, transmission and singular crack problems, 2008), we focus on new Mellin edge quantisations of the Dirichlet-to-Neumann operator on the Neumann side of the boundary and employ a pseudo-differential calculus of corresponding boundary value problems without the transmission property at the interface. This allows us to construct parametrices for the original mixed problem in a new and transparent way.},
  language  = {en}
}
@article{ChangHedayatMahmoudiSchulze2017,
  author    = {Chang, Der-Chen and Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang},
  title     = {Singular degenerate operators},
  series = {Applicable analysis : an international journal},
  volume    = {96},
  journal   = {Applicable analysis : an international journal},
  number    = {14},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {0003-6811},
  doi       = {10.1080/00036811.2017.1336546},
  pages     = {2434 -- 2456},
  year      = {2017},
  abstract  = {We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.},
  language  = {en}
}
@article{ChangMahmoudiSchulze2018,
  author    = {Chang, Der-Chen and Mahmoudi, Mahdi Hedayat and Schulze, Bert-Wolfgang},
  title     = {Volterra operators in the edge-calculus},
  series = {Analysis and Mathematical Physics},
  volume    = {8},
  journal   = {Analysis and Mathematical Physics},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1664-2368},
  doi       = {10.1007/s13324-018-0238-4},
  pages     = {551 -- 570},
  year      = {2018},
  abstract  = {We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).},
  language  = {en}
}
@article{ChangQianSchulze2015,
  author    = {Chang, Der-Chen and Qian, Tao and Schulze, Bert-Wolfgang},
  title     = {Corner Boundary Value Problems},
  series = {Complex analysis and operator theory},
  volume    = {9},
  journal   = {Complex analysis and operator theory},
  number    = {5},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1661-8254},
  doi       = {10.1007/s11785-014-0424-9},
  pages     = {1157 -- 1210},
  year      = {2015},
  abstract  = {Boundary value problems on a manifold with smooth boundary are closely related to the edge calculus where the boundary plays the role of an edge. The problem of expressing parametrices of Shapiro-Lopatinskij elliptic boundary value problems for differential operators gives rise to pseudo-differential operators with the transmission property at the boundary. However, there are interesting pseudo-differential operators without the transmission property, for instance, the Dirichlet-to-Neumann operator. In this case the symbols become edge-degenerate under a suitable quantisation, cf. Chang et al. (J Pseudo-Differ Oper Appl 5(2014):69-155, 2014). If the boundary itself has singularities, e.g., conical points or edges, then the symbols are corner-degenerate. In the present paper we study elements of the corresponding corner pseudo-differential calculus.},
  language  = {en}
}
@article{ChangSchulze2017,
  author    = {Chang, Der-Chen and Schulze, Bert-Wolfgang},
  title     = {Ellipticity on spaces with higher singularities},
  series = {Science China Mathematics},
  volume    = {60},
  journal   = {Science China Mathematics},
  number    = {11},
  publisher = {Science China Press},
  address   = {Beijing},
  issn      = {1674-7283},
  doi       = {10.1007/s11425-016-0519-9},
  pages     = {2053 -- 2076},
  year      = {2017},
  abstract  = {We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata.},
  language  = {en}
}
@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}
}
@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}
}
@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}
}