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Information × Registration Number 0223U004798, 0123U102663 , R & D reports Title Symmetries in algebraic and topological structures on infinite-dimensional analytic manifolds and their possible applications popup.stage_title Head Zahorodniuk Andrii V., д.ф.-м.н. Registration Date 04-12-2023 Organization Vasyl Stefanyk Precarpathian National University popup.description2  Report SRW: 241 p., there are 11 chapters. Research object – infinite-dimensional manifolds, symmetric, supersymmetric analytic and Lipschitz functions on Banach spaces, block-symmetric mappings. The aim of the Project is to establish the properties of spectra (and their subsets) of algebras of S-invariant analytic functions of bounded type on a Banach space X for different semigroups of symmetry S and spaces X; the consideration of specific algebras of symmetric, block-symmetric and supersymmetric analytic functions with respect to discrete and continuum symmetry semigroups; the generalization of the results obtained for the algebras of analytic functions in Banach space generated by a countable family of polynomials; the research of new approaches for the creation of public key encryption algorithms, construction of generators of pseudo-random variables, image recognition algorithms and new mathematical tools for modeling the processes of quantum mechanics. Results and novelty: The spectra of algebras of symmetric analytic functions on tensor products of spaces lp is investigated. The representation of the spectra in subspaces of entire functions of several complex variables is given. Analytic structures on the spectrum of algebra of block-symmetric analytic functions on the space L∞ (U) are described. The hypothesis that each block-symmetric analytic function on L∞ (U) will be of bounded type is confirmed. The real case and the case of *-analytic functions are considered. The spectra of algebras of supersymmetric analytic functions on two-sided spaces lp is investigated. The differentiation in these algebras is described. The applications to the construction of algorithms in information theory are found . The algebras of analytic functions of bounded type generated by a countable family of polynomials are investigated. The conditions of isomorphism of such algebras and the general properties of their spectra are described. Applications of the received Product Description popup.authors Baziv Natalia Mykolayivna Bandura Andriy Ivanovich Burtniak Ivan Volodymyrovych Vasylyshyn(Halushchak) Svitlana Igorivna Vasylyshyn Taras V. Hladkyy Volodymyr Yaroslavovych Kopylchuk Liubov V Kravtsiv Victoria V. Labachuk Oksana Vasylivna Martsinkiv Mariia Volodymyrivna Novosad Zoriana G Chernega Iryna Volodymyrivna Chopyuk Yurii Yuriyovych Shlikhutka Bohdan T popup.nrat_date 2023-12-04 Close