
doi: 10.1007/bf00972775
The author considers the measure \(n_ A\) associated to the sequence \(A=\{a^{(k)}\}\), where we may have \(a^{(k)}=a^{(h)}\) for \(k\neq h\), the carrier of \(n_ A\) is \(A\) and \(n_ a(\{a^{(k)}\})\) represents the number of terms of the sequence \(A\) corresponding to the same point \(a^{(k)}\in\mathbb{C}^ n\). If \(Z_ f=\{z\in\mathbb{C}^ n: f(z)=0\}=\bigcup_{k=1}^ \infty H_ k\), where \(H_ k=\{z\in\mathbb{C}^ n: \langle z,a^{(k)}\rangle=| a^{(k)}|^ 2\}\), \(\langle a,w\rangle =z_ 1\bar {w_ 1}+\dots+z_ l\bar w^ l\) and \(a^{(k)}\) is the foot of the perpendicular from the origin onto \(H_ k\), then, the sequence \(A_ f=A\), with the corresponding meaning of \(a^{(k)}\), is called the sequence associated to \(f\). Using this measure, he introduces the concept of function with regular set of planes of zeros and establishes that this class of functions has a regular growth and describes the radial indicator [cf. \textit{P. Z. Agranovich}, Teor. Funkts. Funkts. Anal. Prilozh. 30, 3-13 (1978; Zbl 0449.32003)] by means of some integral representations.
Entire functions of several complex variables, Integral representations; canonical kernels (Szegő, Bergman, etc.), distribution, growth theorems, Nevanlinna theory; growth estimates; other inequalities of several complex variables, entire functions
Entire functions of several complex variables, Integral representations; canonical kernels (Szegő, Bergman, etc.), distribution, growth theorems, Nevanlinna theory; growth estimates; other inequalities of several complex variables, entire functions
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