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Abstract <p> 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. </p>

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On the Analytical Representation of Two Classes of Homogeneous Polynomials

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • Z. A. Kusraeva,
  • V. A. Tamaeva

摘要

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.