TY - JOUR
AU - Kravtsiv, V.V.
PY - 2020/06/12
Y2 - 2020/09/20
TI - Analogues of the Newton formulas for the block-symmetric polynomials on $\ell_p(\mathbb{C}^s)$
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 12
IS - 1
SE - Scientific articles
DO - 10.15330/cmp.12.1.17-22
UR - https://scijournals.pnu.edu.ua/index.php/cmp/article/view/3864
SP - 17-22
AB - The classical Newton formulas gives recurrent relations between algebraic bases of symmetric polynomials. They are true, of course, for symmetric polynomials on infinite-dimensional Banach sequence spaces.In this paper, we consider block-symmetric polynomials (or MacMahon symmetric polynomials) on Banach spaces $\ell_p(\mathbb{C}^s),$ $1\le p\le \infty.$ We prove an analogue of the Newton formula for the block-symmetric polynomials for the case $p=1.$ In the case $1< p$ we have no classical elementary block-symmetric polynomials. However, we extend the obtained Newton type formula for $\ell_1(\mathbb{C}^s)$ to the case of $\ell_p(\mathbb{C}^s),$ $1< p\le \infty$, and in this way we found a natural definition of elementary block-symmetric polynomials on $\ell_p(\mathbb{C}^s).$
ER -