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

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

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

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Schinzel, Andrzej. On a decomposition of polynomials in several variables. Journal de théorie des nombres de Bordeaux, Tome 14 (2002) no. 2, pp. 647-666. http://archive.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 | Zbl

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

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

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

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

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

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

[8] B. Reznick, Sums of powers of complex linear forms, unpublished manuscript of 1992.