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Matematicheskie Zametki, 2020, Volume 107, Issue 1, Pages 59–73
DOI: https://doi.org/10.4213/mzm12053
(Mi mzm12053)
 

This article is cited in 1 scientific paper (total in 1 paper)

On a Multilinear Functional Equation

A. A. Illarionovab

a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
b Pacific National University, Khabarovsk
Full-text PDF (571 kB) Citations (1)
References:
Abstract: The following functional equation is solved:
$$ f(x_1+z)\dotsb f(x_2+z)f(x_1+\dotsb+x_{s-1}-z) =\phi_1(x)\psi_1(z)+\dotsb+\phi_m(x)\psi_m(z), $$
where $x=(x_1,\dots,x_{s-1})$, for the unknowns $f,\psi_j\colon\mathbb C\to\mathbb C$ and $\phi_j\colon\mathbb C^{s-1}\to\mathbb C$ for $s\ge 3$ and $m\le 4s-5$.
Keywords: functional equation, theta function, Weierstrass sigma function, elliptic function, addition theorems, multilinear functional-differential operators.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00638
This work was supported by the Russian Foundation for Basic Research under grant 18-01-00638.
Received: 24.04.2018
Revised: 05.09.2018
English version:
Mathematical Notes, 2020, Volume 107, Issue 1, Pages 80–92
DOI: https://doi.org/10.1134/S0001434620010083
Bibliographic databases:
Document Type: Article
UDC: 517.968+517.583
Language: Russian
Citation: A. A. Illarionov, “On a Multilinear Functional Equation”, Mat. Zametki, 107:1 (2020), 59–73; Math. Notes, 107:1 (2020), 80–92
Citation in format AMSBIB
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Математические заметки Mathematical Notes
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