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 Vladikavkaz. Mat. Zh., 2014, Volume 16, Number 4, Pages 49–53 (Mi vmj521)

Homogeneous polynomials, root mean power, and geometric means in vector lattices

Z. A. Kusraeva

South Mathematical Institute of VSC RAS, Vladikavkaz, Russia

Abstract: 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.

Key words: vector lattice, homogeneous polynomial, linearization of a polynomial, root mean power, geometric mean.

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UDC: 517.98

Citation: Z. A. Kusraeva, “Homogeneous polynomials, root mean power, and geometric means in vector lattices”, Vladikavkaz. Mat. Zh., 16:4 (2014), 49–53

Citation in format AMSBIB
\Bibitem{Kus14} \by Z.~A.~Kusraeva \paper Homogeneous polynomials, root mean power, and geometric means in vector lattices \jour Vladikavkaz. Mat. Zh. \yr 2014 \vol 16 \issue 4 \pages 49--53 \mathnet{http://mi.mathnet.ru/vmj521}