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Information × Registration Number 0224U032218, 0123U103606 , R & D reports Title Investigations of properties of algebras of symmetric functions on Banach spaces popup.stage_title Head Vasylyshyn Taras V., Доктор фізико-математичних наук Registration Date 14-08-2024 Organization Vasylyshyn Taras V. popup.description2  The object of research is algebras of symmetric functions on Banach spaces. The aim of the work is to investigate the spectra of topological algebras of symmetric functions on rearrangement-invariant Banach spaces of Lebesgue-measurable functions and on Banach spaces of sequences with symmetric bases. Research methods – methods of the theory of analytic functions on infinite-dimensional spaces, theory of Fréchet algebras. The work examines a wide class of algebras of symmetric functions on Banach spaces. Some general results are established for algebras of symmetric polynomials and algebras of entire symmetric functions on these spaces. In particular, the structures of the spectra of some algebras of entire symmetric functions of bounded type on Banach spaces are investigated. Algebras of block-symmetric and weakly symmetric functions are also investigated. These results are applied to algebras of symmetric functions on complex Banach spaces of Lebesgue-measurable functions. The class of supersymmetric polynomials on sequence spaces is also considered, and the connection of these polynomials with partition functions for a quantum mechanical system, which consists of both bosons and fermions, is established. The results of the work were published in 4 works in scientific publications, indexed in the databases Scopus and Web of Science. Product Description popup.authors popup.nrat_date 2024-08-14 Close