Geodesic
Solutions of a functional equation concerning with trilinear differential operators
Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 2, pp. 169-180 Cet article a éte moissonné depuis la source Math-Net.Ru

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We solve the functional equation $$ f(x+z)f(y+z)f(x+y-z) = \sum_{j=1}^m \phi_j(x,y)\psi_j(z) $$ for $m\le 5$. 
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A. A. Illarionov. Solutions of a functional equation concerning with trilinear differential operators. Dalʹnevostočnyj matematičeskij žurnal, Tome 16 (2016) no. 2, pp. 169-180. http://geodesic.mathdoc.fr/item/DVMG_2016_16_2_a5/

[1] V.M. Bukhshtaber, D.V. Leikin, “Trilineinye funktsionalnye uravneniya”, UMN, 60:2 (2005), 151–152 | DOI | MR | Zbl

[2] V.A. Bykovskii, “Giperkvazimnogochleny i ikh prilozheniya”, Funkts. analiz i ego pril., 50:3 (2016), 34–46 | DOI

[3] E.T. Uitteker, Dzh.N. Vatson, Kurs sovremennogo analiza, v. 2, Fizmatgiz, M., 1963

[4] S. Stoilov, Teoriya funktsii kompleksnogo peremennogo, v. 1, Izd-vo inostr. liter., M., 1962

[5] R. Rochberg, L. Rubel, “A Functional Equation”, Indiana Univ. Math. J., 41:2 (1992), 363–376 | DOI | MR | Zbl

[6] M. Bonk, “The addition formula for theta function”, Aequationes Math., 53:1–2 (1997), 54–72 | DOI | MR | Zbl

[7] M. Bonk, “The addition theorem of Weierstrass's sigma function”, Math. Ann., 298:1 (1994), 591–610 | DOI | MR | Zbl

[8] M. Bonk, “The Characterization of Theta Functions by Functional Equations”, Abh. Math. Sem. Univ. Hamburg, 65 (1995), 29–55 | DOI | MR | Zbl

[9] A.A. Illarionov, “Funktsionalnoe uravnenie i sigma-funktsiya Veiershtrassa”, Funkts. analiz i ego pril., 50:4 (2016), 43–54 | DOI

[10] G. Peano, “Sur le determinant wronskien”, Mathesis IX, 1889, 110–112 | Zbl