TY  - JOUR
A1  - Alsaedy, Ammar
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - A Hilbert Boundary Value Problem for Generalised Cauchy-Riemann Equations
JF  - Advances in applied Clifford algebras
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.
KW  - Dirac operator
KW  - Clifford algebra
KW  - Riemann-Hilbert problem
KW  - Fredholm operators
Y1  - 2017
U6  - https://doi.org/10.1007/s00006-016-0676-8
SN  - 0188-7009
SN  - 1661-4909
VL  - 27
SP  - 931
EP  - 953
PB  - Springer
CY  - Basel
ER  -