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
Related Articles
- EP ID EP535545
- DOI 10.15330/cmp.10.2.395-401
- Views 70
- Downloads 0
Lateral continuity and orthogonally additive operators
We generalize the notion of a laterally convergent net from increasing nets to general ones and study the corresponding lateral continuity of maps. The main result asserts that, the lateral continuity of an orthogonally...
A multidimensional generalization of the Rutishauser qd-algorithm
In this paper the regular multidimensional C-fraction with independent variables, which is a generalization of regular C-fraction, is considered. An algorithm of calculation of the coefficients of the regular multidimens...
Periodic words connected with the Fibonacci words
In this paper we introduce two families of periodic words (FLP-words of type 1 and FLP-words of type 2) that are connected with the Fibonacci words and investigated their properties.
On generalized complex space forms satisfying certain curvature conditions
We study Ricci soliton $(g,V,\lambda)$ of generalized complex space forms when the Riemannian, Bochner and $W_2$ curvature tensors satisfy certain curvature conditions like semi-symmetric, Einstein semi-symmetric, Ricci...
A Worpitzky boundary theorem for branched continued fractions of the special form
For a branched continued fraction of a special form we propose the limit value set for the Worpitzky-like theorem when the element set of the branched continued fraction is replaced by its boundary.