An interpolation characterization of domains of holomorphy

摘要

A connected open set OMEGA is contained in C is called a .domain of holomorphy, if there do not exist nonempty open sets OMEGA_1, OMEGA_2 withOMEGA_2 connected, so that for every u that is holomorphic on OMEGA there is a u_2 holomorphic on OMEGA_2 with u = u_2 on OMEGA_1. This definition is complicated. Generally speaking, a domain of hotomorphy is a domain of definition of holomorphic functions in the sense that there exists a holomorphic function on fi that cannot be holomor-phically continued to any slightly large open set. Domains of holomorphy play a very important role in the theory of several complex variables. There are many different characterizations for domains of holomorphy—geometrical, analytical or algebraical, each takes its different efficient functions in treating various concrete problems of several complex variables (see ref. [1], for example) . In this note, we use the skills of sheaf theory to give a characterization of domains of holomorphy by means of some interpolation property.