Almost periodic currents, chains and divisors in tube domains (Q2782540)

The authors introduce and study almost periodic currents and holomorphic chains in tube domains of \(\mathbb{C}^n\). NEWLINENEWLINENEWLINEThe paper is organized as follows. In Section 1 preliminaries on almost periodic functions and distributions are given, and almost periodic currents are introduced and studied. Theorems 1.2 and 1.3 are consequences of the corresponding results from a paper of Ronkin on almost periodic distributions. Non-trivial points appear when applying almost periodic currents to the study of almost periodic holomorphic mappings, divisors, and holomorphic chains. Such problems are treated in the following sections. NEWLINENEWLINENEWLINESection 2 is devoted to almost periodic holomorphic currents. We formulate the statement on almost periodic currents connected with almost periodic holomorphic mappings. Let \(R_q(G)\) be the set of all regular almost periodic holomorphic mappings of the tube domain \(T_G\) into \(\mathbb{C}^q\). If \(f\in R_q(G)\) then the currents \(\log |f|^2(dd^c\log |f|^2)^l\), \(l<q\), and \((dd^c\log |f|^2)^l\), \(l<q\), are almost periodic in \(T_G\). NEWLINENEWLINENEWLINEJessen functions of almost periodic divisors are considered in Section 3, and the problem of realizability of almost periodic divisors is studied in Section 4.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00031].