@unpublished{FedchenkoTarkhanov2013,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Class of Toeplitz Operators in Several Variables},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-68932},
  year      = {2013},
  abstract  = {We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.},
  language  = {en}
}
@article{FedchenkoTarkhanov2015,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Class of Toeplitz Operators in Several Variables},
  series = {Advances in applied Clifford algebras},
  volume    = {25},
  journal   = {Advances in applied Clifford algebras},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {0188-7009},
  doi       = {10.1007/s00006-015-0546-9},
  pages     = {811 -- 828},
  year      = {2015},
  abstract  = {We introduce the concept of Toeplitz operator associated with the Laplace-Beltrami operator on a compact Riemannian manifold with boundary. We characterise those Toeplitz operators which are Fredholm, thus initiating the index theory.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {A Lefschetz fixed point theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25073},
  year      = {1997},
  abstract  = {We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSternin1998,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25296},
  year      = {1998},
  abstract  = {For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space.},
  language  = {en}
}
@unpublished{FedchenkoTarkhanov2014,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {An index formula for Toeplitz operators},
  volume    = {3},
  number    = {12},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-72499},
  pages     = {24},
  year      = {2014},
  abstract  = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.},
  language  = {en}
}
@article{FedchenkoTarkhanov2015,
  author    = {Fedchenko, Dmitri and Tarkhanov, Nikolai Nikolaevich},
  title     = {An index formula for Toeplitz operators},
  series = {Complex variables and elliptic equations},
  volume    = {60},
  journal   = {Complex variables and elliptic equations},
  number    = {12},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2015.1050007},
  pages     = {1764 -- 1787},
  year      = {2015},
  abstract  = {We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first-order partial differential equations in a bounded domain in R-n with smooth boundary.},
  language  = {en}
}
@article{KhalilSchulze2017,
  author    = {Khalil, Sara and Schulze, Bert-Wolfgang},
  title     = {Boundary problems on a manifold with edge},
  series = {Asian-European Journal of Mathematics},
  volume    = {10},
  journal   = {Asian-European Journal of Mathematics},
  number    = {2},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557117500875},
  pages     = {43},
  year      = {2017},
  abstract  = {We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel's theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.},
  language  = {en}
}
@unpublished{FedchenkoTarkhanov2016,
  author    = {Fedchenko, Dmitry and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems for elliptic complexes},
  volume    = {5},
  number    = {3},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-86705},
  pages     = {12},
  year      = {2016},
  abstract  = {The aim of this paper is to bring together two areas which are of great importance for the study of overdetermined boundary value problems. The first area is homological algebra which is the main tool in constructing the formal theory of overdetermined problems. And the second area is the global calculus of pseudodifferential operators which allows one to develop explicit analysis.},
  language  = {en}
}
@article{BaerBandara2022,
  author    = {B{\"a}r, Christian and Bandara, Lashi},
  title     = {Boundary value problems for general first-order elliptic differential operators},
  series = {Journal of functional analysis},
  volume    = {282},
  journal   = {Journal of functional analysis},
  number    = {12},
  publisher = {Elsevier},
  address   = {Amsterdam [u.a.]},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2022.109445},
  pages     = {69},
  year      = {2022},
  abstract  = {We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods.},
  language  = {en}
}
@unpublished{SavinSchulzeSternin2000,
  author    = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Elliptic operators in subspaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25701},
  year      = {2000},
  abstract  = {We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.},
  language  = {en}
}