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Information × Registration Number 0220U104194, 0120U103996 , R & D reports Title Symmetries in algebraic and topological structures on infinitely dimensional analytic manifolds and their possible applications popup.stage_title Head Zagorodniuk Andrii V., Registration Date 14-12-2020 Organization Vasyl Stefanyk Precarpathian National University, State Higher Educational Institution popup.description2 Keywords: analytic functions on Banach spaces, symmetric analytic functions, analytic varieties, invariants of operator semigroups, hypercyclic operators, functions of bounded index. Object of research: infinite-dimensional varieties, symmetric mappings. The aim of the project is a complete description of the analytical structure of the spectrum of algebras of symmetric analytic functions of bounded type on spaces of sequences and functions, application of supersymmetric analytic functions to algebras. Research methodology. The algebras of analytic functions in Banach space generated by a countable family of polynomials are considered. In general, there is a semigroup of operators with respect to which functions of a given algebra will be invariant. The general properties of the spectra of countably generated algebras, the conditions for the existence of a group of symmetry and isomorphism between algebras will be studied. In the first stage of the Project it is proved that the radius of the homomorphism function of the value at the algebra point of integer symmetric functions of bounded type on l1 is equal to the norm of this point, and that each character of this algebra is represented as a Hadamard product or exponent in the functions of one variable. The hypothesis that each symmetric analytic function on the space L∞ is of bounded type is tested and an example of a symmetric analytic function on L∞ that is not a function of bounded type is constructed. This example exists both in the complex and in the real case. Also, new classes of analytic functions of unlimited type on Banach spaces are found. It is shown that the differentiations that generate a semigroup of symmetric shifts are continuous. The conditions of self-coupling and relations for operators of differentiation and multiplication by function are established. The conditions of hypercyclicity of operators of differentiation and symmetric shift are found. New classes of hypercyclic operators are const Product Description popup.authors Bandura Andrii I Vasylyshyn Taras V. Kopylchuk Liubov V Kravtsiv Victoria V. Martsinkiv Mariia V Novosad Zoriana G Cherneha Iryna V Chopiuk Yurii Yu Shlikhutka Bohdan T popup.nrat_date 2020-12-14 Close