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

Анотація

For a holomorphic almost periodic mapping f from a tube domain of C ⁿ, into C ^q, the properties of its Jessen function, i.e., the mean value of the function 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 Ф_l on plurisubharmonic functions are introduced in a way that for a smooth function u, (Ф _l [u]) ^l(dd ^c | z | ²) ⁿ =(dd ^c u) ^lΛ(dd ^c | z | ²) ^n-l