# Algebras of weakly symmetric functions on spaces of Lebesgue measurable functions

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.

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**(2), 411-419.