@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{LyuQianSchulze2015,
  author    = {Lyu, Xiaojing and Qian, Tao and Schulze, Bert-Wolfgang},
  title     = {Order filtrations of the edge algebra},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {6},
  journal   = {Journal of pseudo-differential operators and applications},
  number    = {3},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-015-0126-8},
  pages     = {279 -- 305},
  year      = {2015},
  abstract  = {By edge algebra we understand a pseudo-differential calculus on a manifold with edge. The operators have a two-component principal symbolic hierarchy which determines operators up to lower order terms. Those belong to a filtration of the corresponding operator spaces. We give a new characterisation of this structure, based on an alternative representation of edge amplitude functions only containing holomorphic edge-degenerate Mellin symbols.},
  language  = {en}
}
@phdthesis{Lyu2016,
  author    = {Lyu, Xiaojing},
  title     = {Operators on singular manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-103643},
  school      = {Universit{\"a}t Potsdam},
  pages     = {117},
  year      = {2016},
  abstract  = {We study the interplay between analysis on manifolds with singularities and complex analysis and develop new structures of operators based on the Mellin transform and tools for iterating the calculus for higher singularities. We refer to the idea of interpreting boundary value problems (BVPs) in terms of pseudo-differential operators with a principal symbolic hierarchy, taking into account that BVPs are a source of cone and edge operator algebras. The respective cone and edge pseudo-differential algebras in turn are the starting point of higher corner theories. In addition there are deep relationships between corner operators and complex analysis. This will be illustrated by the Mellin symbolic calculus.},
  language  = {en}
}
@article{LyuSchulze2016,
  author    = {Lyu, Xiaojing and Schulze, Bert-Wolfgang},
  title     = {Mellin Operators in the Edge Calculus},
  series = {Complex analysis and operator theory},
  volume    = {10},
  journal   = {Complex analysis and operator theory},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1661-8254},
  doi       = {10.1007/s11785-015-0511-6},
  pages     = {965 -- 1000},
  year      = {2016},
  abstract  = {A manifold M with smooth edge Y is locally near Y modelled on X-Delta x Omega for a cone X-Delta := ( (R) over bar (+) x X)/({0} x X) where Xis a smooth manifold and Omega subset of R-q an open set corresponding to a chart on Y. Compared with pseudo-differential algebras, based on other quantizations of edge-degenerate symbols, we extend the approach with Mellin representations on the r half-axis up to r = infinity, the conical exit of X-boolean AND = R+ x X (sic) (r, x) at infinity. The alternative description of the edge calculus is useful for pseudo-differential structures on manifolds with higher singularities.},
  language  = {en}
}