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Sufficient conditions of boundedness of $$L$$-index in joint variables. (English) Zbl 1353.30030
Summary: A concept of boundedness of $$L$$-index in joint variables [see M. T. Bordulyak, Mat. Stud. 4, 53–58 (1995; Zbl 1023.32500)] is generalised for $$L(z)= (l_1(z),\dots, l_n(z))$$, $$z\in\mathbb{C}^n$$. We proved criteria of boundedness of $$L$$-index in joint variables and established a connection between the classes of entire functions of bounded $$l_j$$-index in each direction $$e_j$$ and functions of bounded $$L$$-index in joint variables.
We deduce new sufficient conditions of boundedness of $$L$$-index in joint variables. The obtained restrictions describe the behaviour of logarithmic derivative in each variable and the distribution of zeros.

MSC:
 30D20 Entire functions of one complex variable (general theory) 32A15 Entire functions of several complex variables 32A60 Zero sets of holomorphic functions of several complex variables
Zbl 1023.32500
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