Algebras of weakly symmetric functions on spaces of Lebesgue measurable functions

Authors

  • I.V. Burtnyak Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • Yu.Yu. Chopyuk Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • S.I. Vasylyshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
  • T.V. Vasylyshyn Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, Ukraine
https://doi.org/10.15330/cmp.15.2.411-419

Keywords:

symmetric function, weakly symmetric function, analytic function on an infinite dimensional space, space of Lebesgue measurable functions
Published online: 2023-11-14

Abstract

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.

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How to Cite
(1)
Burtnyak, I.; Chopyuk, Y.; Vasylyshyn, S.; Vasylyshyn, T. Algebras of Weakly Symmetric Functions on Spaces of Lebesgue Measurable Functions. Carpathian Math. Publ. 2023, 15, 411-419.