Pluriharmonic continuation in a fixed direction

Questions of the holomorphic and the pluriharmonic continuation of functions in a fixed direction are considered. It is shown that in the continuation of pluriharmonic functions from a boundary system of lines one usually confronts many-valued extensions. This phenomenon is directly related to a counterexample of Levenberg and Slodkowski demonstrating that there exists no potential for a pseudoconvex set in the general case.