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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
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.
Received: 24.04.2018 Revised: 05.09.2018
Citation:
A. A. Illarionov, “On a Multilinear Functional Equation”, Mat. Zametki, 107:1 (2020), 59–73; Math. Notes, 107:1 (2020), 80–92
Linking options:
https://www.mathnet.ru/eng/mzm12053https://doi.org/10.4213/mzm12053 https://www.mathnet.ru/eng/mzm/v107/i1/p59
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Abstract page: | 357 | Full-text PDF : | 59 | References: | 42 | First page: | 11 |
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