Geodesic
Homogeneous polynomials, root mean power, and geometric means in vector lattices
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 49-53 
Z. A. Kusraeva. Homogeneous polynomials, root mean power, and geometric means in vector lattices. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 49-53. http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a5/
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     author = {Z. A. Kusraeva},
     title = {Homogeneous polynomials, root mean power, and geometric means in vector lattices},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {49--53},
     year = {2014},
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     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

It is proved that for a homogeneous orthogonally additive polynomial $P$ of degree $s\in\mathbb N$ from a uniformly complete vector lattice $E$ to some convex bornological space the equations $P(\mathfrak S_s(x_1,\ldots,x_N))= P(x_1)+\ldots+P(x_N)$ and $P(\mathfrak G(x_1,\ldots,x_s))=\check P(x_1,\ldots,x_s)$ hold for all positive $x_1,\ldots,x_s\in E$, where $\check P$ is an $s$-linear operator generating $P$, while $\mathfrak S_s(x_1,\ldots,x_N)$ and $\mathfrak G(x_1,\ldots,x_s)$ stand respectively for root mean power and geometric mean in the sense of homogeneous functional calculus.

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