Representation of functions by logarithmic potential and reducibility of analytic functions of several variables (Q1922177)

The paper is devoted to the problem of representation of functions by the potential \[ \int \ln |P_\alpha |d\mu (\alpha) \tag{1} \] where, for every \(\alpha\), \(P_\alpha\) is a holomorphic polynomial of degree \(\leq m\), \(m\) a fixed integer and \(\mu\) a positive measure. The necessary and sufficient condition that a given plurisubharmonic or a subharmonic function admits the representation by the potential (1) is given in terms of the generalized Radon transform. This representation is applied to the reducibility problem for analytic functions.