@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}
}