On the Analytical Representation of Two Classes of Homogeneous Polynomials

Z. A. Kusraeva^a, V. A. Tamaeva<sup>a

a</sup> Vladikavkaz Scientific Centre of the Russian Academy of Sciences

Abstract: The objective of this paper is to obtain an analytical representation for two classes of homogeneous orthogonally additive polynomials acting on vector lattices and defined in mixed terms of the norm and order. The first class is characterized by the property of order boundedness on the unit ball, and the other by the presence of a majorant. The proof relies on the linearization method using the construction of the power of a vector lattice.

Keywords: vector lattice, homogeneous polynomial, linearization, power of a vector lattice, abstract norm, majorant, weakly measurable vector-function.

UDC: 517

MSC: 46A16, 46B42, 46G25, 47A40, 47H60

Received: 06.12.2024
Revised: 09.02.2025

DOI: 10.4213/mzm14588

 English version: Mathematical Notes, 2025, 118:1, 108–118

Bibliographic databases:

•