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Information × Registration Number 0226U001620, (0123U101791) , R & D reports Title Study of algebras generated by symmetric polynomial and rational mappings in Banach spaces popup.stage_title Дослідження алгебр, породжених симетричними поліноміальними та раціональними відображеннями у банахових просторах Head Zagorodnyuk Andriy Vasylovych, д.ф.-м.н. Registration Date 28-01-2026 Organization Vasyl Stefanyk Precarpathian National University popup.description1 The goal of the project is a comprehensive study of algebras of symmetric analytic and rational functions on Banach spaces, fractional mappings from a finite and infinite number of variables, construction of new algorithms for the development of given functions into functional branched chain fractions, establishment of conditions and signs of convergence, estimation of approximation errors, obtaining applications, recognition and machine learning. popup.description2 Keywords: topological algebra, symmetric function, rational function, spectrum, continued fraction. Object of research: Symmetric analytic and rational functions on Banach spaces; algebras of symmetric and supersymmetric analytic functions; spectra of algebras and homomorphisms; continued fractions and their multidimensional generalizations, in particular branched chain fractions, chain fractions in infinitely many variables; functions and recognition algorithms for data sets with diverse structures. Subject of research: The structure and properties of the spectra of algebras of symmetric and supersymmetric analytic and rational functions on Banach spaces; conditions for the approximability of such algebras in spaces of continuous functions; properties and convergence criteria of continued fractions and their multidimensional generalizations; algorithms for constructing continued fractions and their generalizations; expansions of functions and their ratios into multidimensional and infinite-dimensional generalizations of continued fractions; construction of hash functions and recognition algorithms for data sets with diverse structures. The goal of the project is a comprehensive study of algebras of symmetric analytic and rational functions on Banach spaces, fractional mappings from a finite and infinite number of variables, construction of new algorithms for the development of given functions into functional branched chain fractions, establishment of conditions and signs of convergence, estimation of approximation errors, obtaining applications, recognition and machine learning. Product Description popup.authors Antonova Tamara Roman I. Dmytryshyn Taras V. Vasylyshyn Kravtsiv Viktoriia V. Лопушанський Олег Васильович Solomko Andriy Vasylovych Martsinkiv Mariia Volodymyrivna Serhii V. Sharyn Taras P. Hoi Svitlana I. Vasylyshyn Mykhailo M. Osypchuk Sviatoslav I. Nykorovych popup.nrat_date 2026-01-28 Close