  In this paper we analyze the Hilbert boundary-value problem of the theory of
analytic functions for an $(N+1)$-connected circular domain. An exact
series-form solution has already been derived for the case of continuous
coefficients. Motivated by the study of the Hall effect in a multiply connected
plate we extend these results by examining the case of discontinuous
coefficients. The Hilbert problem maps into the Riemann-Hilbert problem for
symmetric piece-wise meromorphic functions invariant with respect to a
symmetric Schottky group. The solution to this problem is derived in terms of
two analogues of the Cauchy kernel, quasiautomorphic and quasimultiplicative
kernels. The former kernel is known for any symmetry Schottky group. We prove
the existence theorem for the second, quasimultiplicative, kernel for any
Schottky group (its series representation is known for the first class groups
only). We also show that the use of an automorphic kernel requires the solution
to the associated real analogue of the Jacobi inversion problem which can be
bypassed if we employ the quasiautomorphic and quasimultiplicative kernels. We
apply this theory to a model steady-state problem on the motion of charged
electrons in a plate with $N+1$ circular holes with electrodes and dielectrics
on the walls when the conductor is placed at right angle to the applied
magnetic field.
