Algebras of weakly symmetric functions on spaces of Lebesgue measurable functions Article Swipe

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Mathematics Pure mathematics Lp space Lebesgue integration Bounded function Measurable function Lebesgue measure Absolute continuity Banach space Mathematical analysis

Ivan Burtnyak , Yu.Yu. Chopyuk , S.I. Vasylyshyn , Taras Vasylyshyn ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.15330/cmp.15.2.411-419 · OA: W4388657476

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.