The Hilbert boundary problem of doubly periodic analytic functions (Q1111727)

The author continues his considerations of doubly quasi-periodic analytic functions. The MQ-functions under consideration are characterized by \[ \phi (z+z\omega_ j)=b_ j\phi (z)\quad (j=1,2). \] Based on an integral representation formula the existence of solutions to the Dirichlet problem is proved via a Fredholm integral equation. Using this result and a so-called MQ-regularization process the Hilbert boundary value problem for elliptic functions is studied.