On holomorphy of functions representable by the logarithmic residue formula (Q1360835)

The main result of the article establishes the holomorphic continuation property for the continuously differentiable functions given on the boundary \(\partial D\) of a bounded domain \(D\subset \mathbb C^n\), \(n>1\), and orthogonal in the sense of integration over \(\partial D\) to the kernels standing in the many-dimensional logarithmic residue formula. The result is applied to studying functions with the holomorphic continuation property along a certain family of curves.