TY - JOUR
AU - Burtnyak, I.V.
AU - Chopyuk, Yu.Yu.
AU - Vasylyshyn, S.I.
AU - Vasylyshyn, T.V.
PY - 2023/11/14
Y2 - 2024/10/14
TI - Algebras of weakly symmetric functions on spaces of Lebesgue measurable functions
JF - Carpathian Mathematical Publications
JA - Carpathian Math. Publ.
VL - 15
IS - 2
SE - Scientific articles
DO - 10.15330/cmp.15.2.411-419
UR - https://journals.pnu.edu.ua/index.php/cmp/article/view/7002
SP - 411-419
AB - <p>In this work, we investigate algebras of block-symmetric and weakly symmetric polynomials and analytic functions on complex Banach spaces of Lebesgue measurable functions, for which the $p$th power of the absolute value is Lebesgue integrable, where $p\in[1,+\infty),$ and Lebesgue measurable essentially bounded functions on $[0,1].$ We construct generating systems of algebras of all weakly symmetric continuous complex-valued polynomials on these spaces. Also we establish conditions under which sets of weakly symmetric analytic functions are algebras.</p>
ER -