TY  - INPR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Hilbert boundary value problem for generalised Cauchy-Riemann equations
N2  - We elaborate a boundary Fourier method for studying an analogue of the Hilbert problem for analytic functions within the framework of generalised Cauchy-Riemann equations. The boundary value problem need not satisfy the Shapiro-Lopatinskij condition and so it fails to be Fredholm in Sobolev spaces. We show a solvability condition of the Hilbert problem, which looks like those for ill-posed
problems, and construct an explicit formula for approximate solutions.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 5 (2016) 1 
KW  - Dirac operator
KW  - Clifford algebra
KW  - Riemann-Hilbert problem
KW  - Fredholm operator
Y1  - 2016
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-86109
SN  - 2193-6943
VL  - 5
IS  - 1
PB  - Universitätsverlag Potsdam
CY  - Potsdam
ER  - 
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  -