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DOI: 10.23671/VNC.2014.4.10260

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

Kusraeva, Z. A.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 4.
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.
Keywords: vector lattice, homogeneous polynomial, linearization of a polynomial, root mean power, geometric mean
Language: Russian Download the full text  
For citation: Kusraeva Z. A.† Homogeneous polynomials, root mean power, and geometric means in vector lattices // Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 16, no. 4, pp. 49-53. DOI 10.23671/VNC.2014.4.10260
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