Symmetric polynomials on the Cartesian power of Lp on the semi-axis
Journal Title: Математичні Студії - Year 2018, Vol 50, Issue 1
Abstract
The paper deals with polynomials in the complex Banach space (Lp[0,+∞))n, which are the nth Cartesian power of the complex Banach space of Lebesgue measurable integrable in a power p complex-valued functions on [0,+∞), where 1≤p≤+∞. It is proved that if p is an integer, then every continuous symmetric polynomial on (Lp[0,+∞))n can be uniquely represented as an algebraic combination of some ``elementary'' p-homogeneous symmetric polynomials. It is also proved that if p is not an integer, then every continuous symmetric polynomial on (Lp[0,+∞))n is constant. Results of the paper can be used for investigations of algebras of symmetric continuous polynomials and of symmetric analytic functions on (Lp[0,+∞))n.
Authors and Affiliations
T. V. Vasylyshyn
Keywords
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- EP ID EP436200
- DOI 10.15330/ms.50.1.93-104
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