TY  - JOUR
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Deformation quantization and boundary value problems
JF  - International journal of geometric methods in modern physics : differential geometery, algebraic geometery, global analysis & topology
N2  - 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.
KW  - Symplectic manifold
KW  - star product
KW  - trace
KW  - index
Y1  - 2016
U6  - https://doi.org/10.1142/S0219887816500079
SN  - 0219-8878
SN  - 1793-6977
VL  - 13
SP  - 176
EP  - 195
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Ly, Ibrahim
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Rado theorem for p-harmonic functions
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - Let A be a nonlinear differential operator on an open set X subset of R-n and S a closed subset of X. Given a class F of functions in X, the set S is said to be removable for F relative to A if any weak solution of A(u) = 0 in XS of class F satisfies this equation weakly in all of X. For the most extensively studied classes F, we show conditions on S which guarantee that S is removable for F relative to A.
KW  - Quasilinear equations
KW  - Removable sets
KW  - p-Laplace equation
Y1  - 2016
U6  - https://doi.org/10.1007/s40590-016-0109-7
SN  - 1405-213X
SN  - 2296-4495
VL  - 22
SP  - 461
EP  - 472
PB  - Springer
CY  - Basel
ER  -