Homogeneous polynomials, root mean power, and geometric means in vector lattices
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 49-53
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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.
@article{VMJ_2014_16_4_a5,
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},
publisher = {mathdoc},
volume = {16},
number = {4},
year = {2014},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a5/}
}
TY - JOUR AU - Z. A. Kusraeva TI - Homogeneous polynomials, root mean power, and geometric means in vector lattices JO - Vladikavkazskij matematičeskij žurnal PY - 2014 SP - 49 EP - 53 VL - 16 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a5/ LA - ru ID - VMJ_2014_16_4_a5 ER -
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/