On a decomposition of polynomials in several variables
Journal de théorie des nombres de Bordeaux, Volume 14 (2002) no. 2, p. 647-666

One considers representation of a polynomial in several variables as the sum of values of univariate polynomials taken at linear combinations of the variables.

On considère la représentation d'un polynôme a plusieurs variables comme une somme de polynômes à une variable en combinaisons linéaires des variables.

@article{JTNB_2002__14_2_647_0,
     author = {Schinzel, Andrzej},
     title = {On a decomposition of polynomials in several variables},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {14},
     number = {2},
     year = {2002},
     pages = {647-666},
     zbl = {1067.11012},
     mrnumber = {2040699},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2002__14_2_647_0}
}
Schinzel, Andrzej. On a decomposition of polynomials in several variables. Journal de théorie des nombres de Bordeaux, Volume 14 (2002) no. 2, pp. 647-666. http://www.numdam.org/item/JTNB_2002__14_2_647_0/

[1] N. Alon, M.B. Nathanson, I. Ruzsa, The polynomial method and restricted sums of congruence classes. J. Number Theory 56 (1996), 404-417. | MR 1373563 | Zbl 0861.11006

[2] P. Diaconis, M. Shahshahani, On nonlinear functions of linear combinations. SIAM J. Sci. Stat. Comput. 5 (1984), 175-191. | MR 731890 | Zbl 0538.41041

[3] W.J. Ellison, A 'Waring's problem' for homogeneous forms. Proc. Cambridge Philos. Soc. 65 (1969), 663-672. | MR 237450 | Zbl 0209.34305

[4] U. Helmke, Waring's problem for binary forms. J. Pure Appl. Algebra 80 (1992), 29-45. | MR 1167385 | Zbl 0791.11020

[5] A. Iarrobino, Inverse system of a symbolic power II. The Waring problem for forms. J. Algebra 174 (1995), 1091-1110. | MR 1337187 | Zbl 0842.11016

[6] B.F. Logan, L.A. Shepp, Optimal reconstruction of a function from its projections. Duke Math. J. 42 (1975), 645-659. | MR 397240 | Zbl 0343.41020

[7] T. Mum, A treatise on the theory of determinants. Dover, 1960. | MR 114826

[8] B. Reznick, Sums of powers of complex linear forms, unpublished manuscript of 1992.