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 57
- Downloads 0
Two-sided inequalities with nonmonotone sublinear operators
The theorems on solutions and their two-sided estimates for one class of nonlinear operator equations x=Fx with nonmonotone operators.
The limiting oscillations of continuous functions
We prove that for any upper semicontinuous function f:F→[0;+∞] defined on the boundary F=¯¯¯¯G∖G of some open set G in metrizable space X there is a continuous function g:G→R such that the limiting oscillation ˜ωg of it...
On the growth of a klasss of Dirichlet series absolutely convergent in half-plane
In terms of generalized orders it is investigated a relation between the growth of a Dirichlet series $F(s)=\sum\limits_{n=1}^{\infty}a_n\exp\{s\lambda_n\}$ with the abscissa of asolute convergence $A\in (-\infty,+\infty...
The nonlocal problem for the 2n differential equations with unbounded operator coefficients and the involution
We study a problem with periodic boundary conditions for a 2n-order differential equation whose coefficients are non-self-adjoint operators. It is established that the operator of the problem has two invariant subspaces...
On the dimension of vertex labeling of k-uniform dcsl of k-uniform caterpillar
A distance compatible set labeling (dcsl) of a connected graph $G$ is an injective set assignment $f : V(G) \rightarrow 2^{X},$ $X$ being a nonempty ground set, such that the corresponding induced function $f^{\oplus} :E...