TY  - JOUR
A1  - Mera, Azal Jaafar Musa
A1  - Tarkhanov, Nikolai
T1  - An elliptic equation of finite index in a domain
JF  - Boletin de la Sociedad Matemática Mexicana
N2  - 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.
KW  - elliptic equation
KW  - Fredholm operator
KW  - index
Y1  - 2022
U6  - https://doi.org/10.1007/s40590-022-00442-7
SN  - 1405-213X
SN  - 2296-4495
VL  - 28
IS  - 2
PB  - Springer International
CY  - New York [u.a.]
ER  - 
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  - Fedchenko, Dmitri
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - An index formula for Toeplitz operators
JF  - Complex variables and elliptic equations
N2  - 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.
KW  - Toeplitz operators
KW  - Fredholm property
KW  - index
KW  - Primary: 47B35
KW  - Secondary: 47L80
Y1  - 2015
U6  - https://doi.org/10.1080/17476933.2015.1050007
SN  - 1747-6933
SN  - 1747-6941
VL  - 60
IS  - 12
SP  - 1764
EP  - 1787
PB  - Routledge, Taylor & Francis Group
CY  - Abingdon
ER  -