A Hilbert boundary value problem for generalised Cauchy-Riemann equations (Q2361362)

The authors 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 thus it fails to be Fredholm in Sobolev spaces. The authors derive a solvability condition of the Hilbert problem, which looks like those for ill-posed problems, and construct an explicit formula for approximate solutions.