@unpublished{FedosovTarkhanov2015,
  author    = {Fedosov, Boris and Tarkhanov, Nikolai Nikolaevich},
  title     = {Deformation quantisation and boundary value problems},
  volume    = {4},
  number    = {5},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-77150},
  pages     = {27},
  year      = {2015},
  abstract  = {We describe a natural construction of deformation quantisation on a compact symplectic manifold with boundary. On the algebra of quantum observables a trace functional is defined which as usual annihilates the commutators. This gives rise to an index as the trace of the unity element. We formulate the index theorem as a conjecture and examine it by the classical harmonic oscillator.},
  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@unpublished{FedchenkoTarkhanov2014,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}
}
@unpublished{NazaikinskiiSternin2002,
  author    = {Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {Relative elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26400},
  year      = {2002},
  abstract  = {This paper is a survey of relative elliptic theory (i.e. elliptic theory in the category of smooth embeddings), closely related to the Sobolev problem, first studied by Sternin in the 1960s. We consider both analytic aspects to the theory (the structure of the algebra of morphismus, ellipticity, Fredholm property) and topological aspects (index formulas and Riemann-Roch theorems). We also study the algebra of Green operators arising as a subalgebra of the algebra of morphisms.},
  language  = {en}
}
@article{MickelssonPaycha2010,
  author    = {Mickelsson, Jouko and Paycha, Sylvie},
  title     = {The logarithmic residue density of a generalized Laplacian},
  series = {Journal of the Australian Mathematical Society},
  volume    = {90},
  journal   = {Journal of the Australian Mathematical Society},
  number    = {1},
  publisher = {Cambridge Univ. Press},
  address   = {Cambridge},
  issn      = {0263-6115},
  doi       = {10.1017/S144678871100108X},
  pages     = {53 -- 80},
  year      = {2010},
  abstract  = {We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold definesan invariant polynomial-valued differential form. We express it in terms of a finite sum of residues ofclassical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas providea pedestrian proof of the Atiyah-Singer formula for a pure Dirac operator in four dimensions and for atwisted Dirac operator on a flat space of any dimension. These correspond to special cases of a moregeneral formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either aCampbell-Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.},
  language  = {en}
}
@article{MeraTarkhanov2022,
  author    = {Mera, Azal Jaafar Musa and Tarkhanov, Nikolai},
  title     = {An elliptic equation of finite index in a domain},
  series = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  volume    = {28},
  journal   = {Boletin de la Sociedad Matem{\´a}tica Mexicana},
  number    = {2},
  publisher = {Springer International},
  address   = {New York [u.a.]},
  issn      = {1405-213X},
  doi       = {10.1007/s40590-022-00442-7},
  pages     = {10},
  year      = {2022},
  abstract  = {We give an example of first order elliptic equation for a complex-valued function in a plane domain which has a finite number of linearly independent solutions for any right-hand side. No boundary value conditions are thus required.},
  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}
}
@unpublished{SavinSternin2005,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Pseudodifferential subspaces and their applications in elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29937},
  year      = {2005},
  abstract  = {The aim of this paper is to explain the notion of subspace defined by means of pseudodifferential projection and give its applications in elliptic theory. Such subspaces are indispensable in the theory of well-posed boundary value problems for an arbitrary elliptic operator, including the Dirac operator, which has no classical boundary value problems. Pseudodifferential subspaces can be used to compute the fractional part of the spectral Atiyah-Patodi-Singer eta invariant, when it defines a homotopy invariant (Gilkey's problem). Finally, we explain how pseudodifferential subspaces can be used to give an analytic realization of the topological K-group with finite coefficients in terms of elliptic operators. It turns out that all three applications are based on a theory of elliptic operators on closed manifolds acting in subspaces.},
  language  = {en}
}
@unpublished{SavinSternin2001,
  author    = {Savin, Anton and Sternin, Boris},
  title     = {Index defects in the theory of nonlocal boundary value problems and the η-invariant},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26146},
  year      = {2001},
  abstract  = {The paper deals with elliptic theory on manifolds with boundary represented as a covering space. We compute the index for a class of nonlocal boundary value problems. For a nontrivial covering, the index defect of the Atiyah-Patodi-Singer boundary value problem is computed. We obtain the Poincar{\´e} duality in the K-theory of the corresponding manifolds with singularities.},
  language  = {en}
}
@misc{MickelssonPaycha2011,
  author    = {Mickelsson, Jouko and Paycha, Sylvie},
  title     = {The logarithmic residue density of a generalized Laplacian},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {649},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41368},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413680},
  pages     = {28},
  year      = {2011},
  abstract  = {We show that the residue density of the logarithm of a generalized Laplacian on a closed manifold defines an invariant polynomial-valued differential form. We express it in terms of a finite sum of residues of classical pseudodifferential symbols. In the case of the square of a Dirac operator, these formulas provide a pedestrian proof of the Atiyah-Singer formula for a pure Dirac operator in four dimensions and for a twisted Dirac operator on a flat space of any dimension. These correspond to special cases of a more general formula by Scott and Zagier. In our approach, which is of perturbative nature, we use either a Campbell-Hausdorff formula derived by Okikiolu or a noncommutative Taylor-type formula.},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1998,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A remark on the index of symmetric operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169},
  year      = {1998},
  abstract  = {We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.},
  language  = {en}
}