Continuous block-symmetric polynomials of degree at most two on the space $(L_\infty)^2$

T.V. Vasylyshyn

doi:10.15330/cmp.8.1.38-43

Continuous block-symmetric polynomials of degree at most two on the space $(L_\infty)^2$

Authors

T.V. Vasylyshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine https://orcid.org/0000-0001-9055-6341

https://doi.org/10.15330/cmp.8.1.38-43

Keywords:

block-symmetric polynomial, symmetric function on $L_\infty$

Published online: 2016-06-30

Abstract

We introduce block-symmetric polynomials on $(L_\infty)^2$ and prove that every continuous block-symmetric polynomial of degree at most two on $(L_\infty)^2$ can be uniquely represented by some "elementary" block-symmetric polynomials.