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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Siberian Mathematica...arrow_drop_down
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Siberian Mathematical Journal
Article . 1991 . Peer-reviewed
License: Springer Nature TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Entire functions of several variables with a regular set of “flat” zeros

Entire functions of several variables with a regular set of ''flat'' zeros
Authors: Papush, D. E.;

Entire functions of several variables with a regular set of “flat” zeros

Abstract

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.

Keywords

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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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
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