@article{Burtnyak_Chopyuk_Vasylyshyn_Vasylyshyn_2023, title={Algebras of weakly symmetric functions on spaces of Lebesgue measurable functions}, volume={15}, url={https://journals.pnu.edu.ua/index.php/cmp/article/view/7002}, DOI={10.15330/cmp.15.2.411-419}, abstractNote={<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>}, number={2}, journal={Carpathian Mathematical Publications}, author={Burtnyak, I.V. and Chopyuk, Yu.Yu. and Vasylyshyn, S.I. and Vasylyshyn, T.V.}, year={2023}, month={Nov.}, pages={411–419} }