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- W3036145196 abstract "The classical Newton formulas gives recurrent relations between algebraic bases of symmetric polynomials. They are true, of course, for symmetric polynomials on infinite-dimensional sequences Banach space. In this paper we consider block-symmetric polynomials (or MacMahon symmetric polynomials) on Banach spaces $ell_p(mathbb{C}^s),$ $1le ple infty.$ 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 $ell_p(mathbb{C}^s),$ $1< ple infty$ and by this way found a natural definition of elementary block-symmetric polynomials on $ell_p(mathbb{C}^s).$" @default.
- W3036145196 created "2020-06-25" @default.
- W3036145196 creator A5003068664 @default.
- W3036145196 date "2020-06-12" @default.
- W3036145196 modified "2023-10-15" @default.
- W3036145196 title "Analogues of the Newton formulas for the block-symmetric polynomials on $ell_p(mathbb{C}^s)$" @default.
- W3036145196 doi "https://doi.org/10.15330/cmp.12.1.17-22" @default.
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