Monge-Ampère operators and Jessen functions of holomorphic almost periodic mappings

Анотація

For a holomorphic almost periodic mapping $f$ from a tube domain of $\mathbf{C}^n$ into $\mathbf{C}^q$, the properties of its Jessen function, i.e., the mean value of the function $\mathrm{log}|f|^2$, are studied. In particular, certain relations between the Jessen function and behavior of the mapping and its zero set are obtained. To this end certain operators $\Phi_l$  on plurisubharmonic functions are introduced in a way that for a smooth function $u$, $$
(\Phi_l[u])^l (dd^c|z|^2)^n=(dd^cu)^l \wedge (dd^c |z|^2)^{n-l}.
$$