Continuation of bianalytic functions of several complex variables

The problem of continuation a bianalytic function of several complex variables in a polycylinder from its values and the values of first-order derivatives on a part of the distinguished boundary is considered. The uniqueness theorem is proved. In the class of bianalytic functions bounded together with first-order derivatives with given constant, an estimate of conditional stability is obtained as an analogue of the theorem on two constants from the theory of functions of a complex variable. A new Cauchy integral formula for bianalytic functions in a polycylinder is obtained. As an application, Carleman’s continuation formula is given for such functions.