Integral representations of functions of several complex variables (Q2377479)

The author presents an integral representation of holomorphic functions in a special class of convex, complete, bicircular domains in \(\mathbb{C}^2\). This representation expresses the values of a holomorphic function in a domain of this class in terms of the values of the following linear differential operator \[ (L_z\circ f)(z)= f(z)+ (z_1- z^0_2){\partial f\over\partial z_2}(z)+ (z_2- z^0_2){\partial f\over\partial z_2}(z) \] on the boundary. The integral representation in question implies the well-known Temlyakov integral representations of the first, second and third kinds.