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Information × Registration Number 0221U106851, 0121U111037 , R & D reports Title Symmetries in algebraic and topological structures on infinitely dimensional analytic manifolds and their possible applications popup.stage_title Head Zagorodnyuk Andriy V., Кандидат фізико-математичних наук Registration Date 21-12-2021 Organization Vasyl Stefanyk Precarpathian National University, State Higher Educational Institution popup.description2  Report SRW: 55p., there are 6 chapters. Research object – infinite-dimensional manifolds, symmetric mappings, block-symmetric analytic mappings The goal of the project is to establish the properties of spectra (and their subsets) of algebras of S-invariant analytic functions of bounded type on Banach space X for various semigroups of symmetry S and spaces X; to investigate the case of algebras of real analytic functions and Lipschitz maps on real Banach spaces; to find application of the obtained results to operators in Hilbert spaces and generalized functions. Research methodology: The existence of a subset of multisets, which is a generalization of the ring of integers, in the spectrum of the algebra of supersymmetric polynomials allows us to apply the methods of number theory and cryptography to construct new encryption algorithms with public key. The invariance of the trace functionals and the Fredholm determinant allow us to apply the theory of symmetric analytic functions to nuclear, p-nuclear, normal, and self-adjoint operators. Both the results of the study of symmetric polynomials and the technique of free Banach spaces were used to study Lipschitz symmetric functions on Banach spaces. The study of symmetric and block-symmetric analytic functions on real Banach spaces has opened the possibility of applying the obtained results to symmetric generalized functions. Results and novelty: connections and correspondences of the constructed theory of symmetric analytic mappings on Banach spaces with the theory of multisets and spectral theory of operators are established. Rings of multisets that arise as submanifolds in the spectrum of supersymmetric analytic functions of bounded type is investigated and proposed an algorithm of encryption with open keys.. Symmetric and block-symmetric analytic mappings on the spaces of self-adjoint Hilbert space operators and homomorphisms in the algebras of such mappings are investigated. Product Description popup.authors Bandura Andriy Ivanovich Burtniak Ivan Volodymyrovych Vasylyshyn(Halushchak) Svitlana Igorivna Vasylyshyn Taras Vasylovych Hladkyi Volodymyr Yaroslavovych Labachuk Oksana Vasylivna Martsinkiv Mariia Volodymyrivna Novosad Zoriana G Cherneha Iryna V. popup.nrat_date 2021-12-21 Close