@unpublished{FedosovSchulzeTarkhanov2003,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {On index theorem for symplectic orbifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26550},
  year      = {2003},
  abstract  = {We give an explicit construction of the trace on the algebra of quantum observables on a symplectic orbifold and propose an index formula.},
  language  = {en}
}
@article{Tarkhanov2016,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {Deformation quantization and boundary value problems},
  series = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology},
  volume    = {13},
  journal   = {International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis \& topology},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {0219-8878},
  doi       = {10.1142/S0219887816500079},
  pages     = {176 -- 195},
  year      = {2016},
  abstract  = {We describe a natural construction of deformation quantization 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@unpublished{FedosovTarkhanov2015,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@unpublished{Tarkhanov2015,
  author    = {Tarkhanov, Nikolai Nikolaevich},
  title     = {A spectral theorem for deformation quantisation},
  volume    = {4},
  number    = {4},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-72425},
  pages     = {8},
  year      = {2015},
  abstract  = {We present a construction of the eigenstate at a noncritical level of the Hamiltonian function. Moreover, we evaluate the contributions of Morse critical points to the spectral decomposition.},
  language  = {en}
}