The Hilbert problem for generalized \(Q\)-holomorphic functions (Q873760)

The author studies a generalized Hilbert problem \[ w_{\bar z} -Qw_z+Aw+B\bar{w}=0\eqno{(\ast)} \] for the unknown \(m\)--by--\(s\) matrix \(w=w(z)\), and where the coefficients are \(m\)-by-\(m\) matrices \(Q=Q(z)\), \(A=A(z)\) and \(B=B(z)\), analytically dependent on \(z\), and subject to some commutativity restraint. When the equation (\(\ast\)) is supplemented with a boundary condition \[ w_+-Hw_-=h \] on a contour \(\Gamma\), a complete solution of this generalized Hilbert boundary problem is given, again subject to some further restraints on matrix-valued functions \(Q,A,B,H\).