Symmetric *-polynomials on Cn
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 2
Abstract
∗-Polynomials are natural generalizations of usual polynomials between complex vector spa\-ces. A ∗-polynomial is a function between complex vector spaces X and Y, which is a sum of so-called (p,q)-polynomials.In turn, for nonnegative integers p and q, a (p,q)-polynomial is a function between X and Y, which is the restrictionto the diagonal of some mapping, acting from the Cartesian power Xp+q to Y, which is linear with respect to every of its first p arguments, antilinear with respect to every of its last q arguments and invariant with respect to permutations of its first p arguments and last q arguments separately. In this work we construct formulas for recovering of (p,q)-polynomial components of ∗-polynomials, acting between complex vector spaces X and Y, by the values of ∗-polynomials. We use these formulas for investigations of ∗-polynomials, acting from the n-dimensional complex vector space Cn to C, which are symmetric, that is, invariant with respect to permutations of coordinates of its argument. We show that every symmetric ∗-polynomial, acting from Cn to C, can be represented as an algebraic combination of some elementary'' symmetric ∗-polynomials. Results of the paper can be used for investigations of algebras, generated by symmetric ∗-polynomials, acting from Cn to C.
Authors and Affiliations
T. V. Vasylyshyn
Keywords
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