@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}
}
@unpublished{AbedSchulze2008,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@unpublished{AbedSchulze2009,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}
}
@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}
}
@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}
}
@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}
}
@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{CalvoSchulze2005,
  author    = {Calvo, D. and Schulze, Bert-Wolfgang},
  title     = {Edge symbolic structures of second generation},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29940},
  year      = {2005},
  abstract  = {Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.},
  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}
}