Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials
This paper investigates the structure and properties of block-symmetric and block-super\-symmetric polynomials in Banach spaces. The study extends classical symmetric polynomial results to infinite-dimensional settings, particularly in sequence spaces such as $\ell_p(\mathbb{C}^s),$ $1\leq p<\inf...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2025-06-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/610 |
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| Summary: | This paper investigates the structure and properties of block-symmetric and block-super\-symmetric polynomials in Banach spaces. The study extends classical symmetric polynomial results to infinite-dimensional settings, particularly in sequence spaces such as $\ell_p(\mathbb{C}^s),$ $1\leq p<\infty$ and spaces of two-sided absolutely summing series of vectors in $\mathbb{C}^s$ for some positive integer $s>1.$ In this paper, we derive analogs of the Waring-Girard formulas for block-symmetric and block-supersymmetric polynomials and explore their combinatorial applications. |
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| ISSN: | 1027-4634 2411-0620 |