Zobrazeno 1 - 10
of 31
pro vyhledávání: '"T.V. Vasylyshyn"'
Autor:
T.V. Vasylyshyn, V.A. Zahorodniuk
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 14, Iss 2, Pp 437-441 (2022)
In this work, we present the notion of a weakly symmetric function. We show that the subset of all weakly symmetric elements of an arbitrary vector space of functions is a vector space. Moreover, the subset of all weakly symmetric elements of some al
Externí odkaz:
https://doaj.org/article/857653c1b3ba479888af1da862ddf532
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 13, Iss 3, Pp 727-733 (2021)
We investigate Lipschitz symmetric functions on a Banach space $X$ with a symmetric basis. We consider power symmetric polynomials on $\ell_1$ and show that they are Lipschitz on the unbounded subset consisting of vectors $x\in \ell_1$ such that $|x_
Externí odkaz:
https://doaj.org/article/75290c8eefbc49b6b41e6e1dd8acba6d
Autor:
T.V. Vasylyshyn
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 13, Iss 2, Pp 340-351 (2021)
The work is devoted to the study of Fréchet algebras of symmetric (invariant under the composition of every of components of its argument with any measure preserving bijection of the domain of components of the argument) analytic functions on Cartes
Externí odkaz:
https://doaj.org/article/309a331f86fb48d9a91d009fbd0405ce
Autor:
T.V. Vasylyshyn
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 12, Iss 1, Pp 5-16 (2020)
This work is devoted to the study of algebras of continuous symmetric polynomials, that is, invariant with respect to permutations of coordinates of its argument, and of $*$-polynomials on Banach spaces $\ell_p(\mathbb{R}^n)$ and $\ell_p(\mathbb{C}^n
Externí odkaz:
https://doaj.org/article/a2d7379900a645b3bcaecb07e39583d4
Autor:
T.V. Vasylyshyn
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 11, Iss 2, Pp 493-501 (2019)
It is known that every continuous symmetric (invariant under the composition of its argument with each Lebesgue measurable bijection of $[0,1]$ that preserve the Lebesgue measure of measurable sets) polynomial on the Cartesian power of the complex Ba
Externí odkaz:
https://doaj.org/article/91a6f55259c34ba49ebcd18836bba693
Autor:
T.V. Vasylyshyn
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 10, Iss 2, Pp 395-401 (2018)
$*$-Polynomials are natural generalizations of usual polynomials between complex vector spaces. 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 intege
Externí odkaz:
https://doaj.org/article/cd4a2876be834a51a22a6d68a7177210
Autor:
T.V. Vasylyshyn
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 10, Iss 1, Pp 206-212 (2018)
A $*$-polynomial is a function on a complex Banach space $X,$ which is a sum of so-called $(p,q)$-polynomials. In turn, for non-negative integers $p$ and $q,$ a $(p,q)$-polynomial is a function on $X,$ which is the restriction to the diagonal of some
Externí odkaz:
https://doaj.org/article/5b14544723e94814b9aa817e9dc58f51
Autor:
T.V. Vasylyshyn
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 9, Iss 2, Pp 198-201 (2018)
It is known that every complex-valued homomorphism of the Fréchet algebra $H_{bs}(L_\infty)$ of all entire symmetric functions of bounded type on the complex Banach space $L_\infty$ is a point-evaluation functional $\delta_x$ (defined by $\delta_x(f
Externí odkaz:
https://doaj.org/article/ac743701d3474bd399bc852a099d98b9
Autor:
T.V. Vasylyshyn
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 9, Iss 1, Pp 22-27 (2017)
It is known that the so-called elementary symmetric polynomials $R_n(x) = \int_{[0,1]}(x(t))^n\,dt$ form an algebraic basis in the algebra of all symmetric continuous polynomials on the complex Banach space $L_\infty,$ which is dense in the Fr\'{e}ch
Externí odkaz:
https://doaj.org/article/6e391ecc02034bb199cdaf9027242af0
Autor:
T.V. Vasylyshyn
Publikováno v:
Karpatsʹkì Matematičnì Publìkacìï, Vol 8, Iss 2, Pp 211-214 (2016)
We consider the question of the possibility to recover a multilinear mapping from the restriction to the diagonal of its extension to a Cartesian power of a space.
Externí odkaz:
https://doaj.org/article/cbf2e9bd96994f278b4bbcef4eb7dc8f