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Information × Registration Number 0226U002247, (0125U000403) , R & D reports Title Algebras of symmetric and weakly symmetric functions on Banach spaces popup.stage_title Дослідження алгебр симетричних і слабко симетричних аналітичних функцій на банахових просторах послідовностей Head Vasylyshyn Taras V., Доктор фізико-математичних наук Registration Date 12-02-2026 Organization Vasyl Stefanyk Precarpathian National University popup.description1 Investigations of algebras of symmetric and weakly symmetric polynomials and analytic functions on Banach spaces popup.description2 The object of research is algebras of symmetric and weakly symmetric polynomials and analytic functions on Banach spaces. A function f on a Banach space X is called S-symmetric, where S is some group of isomorphisms, which act from X to itself, if f(s(x)) = f(x) for all elements x of X and s of S. We obtain the structure of a continuous S-symmetric polynomial on the Banach space of absolutely summable sequences, where S is an arbitrary group of isomorphisms that map the Schauder basis of this space to itself. We describe algebraic bases of algebras of symmetric polynomials on Cartesian products of real Banach spaces of absolutely summable in some (possibly different) powers sequences and of real Banach spaces of Lebesgue integrable in some (possibly different) powers functions on [0,1]. Also we obtain the complete description of the spectrum of some countably generated algebra of entire S-symmetric functions of bounded type on the Banach space of bounded sequences, for some special case of S, such that the generating system contains an infinite number of polynomials for each degree of homogeneity. Product Description popup.authors Vasylyshyn(Halushchak) Svitlana Igorivna Olha B. Hrybel Yurii S. Sharyn Iryna I. Nykorovych popup.nrat_date 2026-02-12 Close