×

zbMATH — the first resource for mathematics

New criteria of boundedness of \(L\)-index in joint variables for entire functions. (Ukrainian. English summary) Zbl 1374.30095
Summary: In the paper we obtain analogues of some criteria of \(L\)-index boundedness in joint variables for an entire function \(F:\mathbb C^n\to\mathbb C\) and a function \(L(z)=(l_1(z),\dots,l_n(z)), z\in\mathbb C^n\). Formerly such theorems were proved by M. T. Bordulyak [Mat. Stud. 4, 53–58 (1995; Zbl 1023.32500)], M. T. Bordulyak and M. M. Sheremeta [Dopov. Nats. Akad. Nauk Ukr., Mat. Pryr. Tekh. Nauky 9, 10–13 (1993)] for the case \(L(z)=(l_1(| z_1|),\dots,l_n(| z_n|))\). We also present new criteria of \(L\)-index boundedness in joint variables, which describe the local behaviour of partial derivatives of an entire function in a polydisc.

MSC:
30D60 Quasi-analytic and other classes of functions of one complex variable
32A10 Holomorphic functions of several complex variables
32A40 Boundary behavior of holomorphic functions of several complex variables
PDF BibTeX XML Cite
Full Text: Link