@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}
}
@article{RungrottheeraLyuSchulze2018,
  author    = {Rungrottheera, Wannarut and Lyu, Xiaojing and Schulze, Bert-Wolfgang},
  title     = {Parameter-dependent edge calculus and corner parametrices},
  series = {Journal of nonlinear and convex analysis : an international journal},
  volume    = {19},
  journal   = {Journal of nonlinear and convex analysis : an international journal},
  number    = {12},
  publisher = {Yokohama Publishers},
  address   = {Yokohama},
  issn      = {1345-4773},
  pages     = {2021 -- 2051},
  year      = {2018},
  abstract  = {Let B be a compact manifold with smooth edge of dimension > 0. We study the interplay between parameter-dependent edge algebra algebra on B and operator families belonging to the corner calculus, and we characterize parametrices in the corner case.},
  language  = {en}
}
@article{HedayatMahmoudiSchulze2018,
  author    = {Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang},
  title     = {A new approach to the second order edge calculus},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {9},
  journal   = {Journal of pseudo-differential operators and applications},
  number    = {2},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-017-0191-2},
  pages     = {265 -- 300},
  year      = {2018},
  abstract  = {We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.},
  language  = {en}
}
@article{FladFladHarutyunyanSchulze2018,
  author    = {Flad, Heinz-J{\"u}rgen and Flad-Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Ellipticity of the quantum mechanical Hamiltonians},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {9},
  journal   = {Journal of pseudo-differential operators and applications},
  number    = {3},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-017-0201-4},
  pages     = {451 -- 467},
  year      = {2018},
  abstract  = {In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis.},
  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}
}