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Information × Registration Number 0222U003503, 0119U100063 , R & D reports Title Algebras of symmetric analytic functions on Banach spaces. Algebraic and analytic structures on the spectra popup.stage_title Head Zahorodniuk Andrii V., Доктор фізико-математичних наук Registration Date 05-04-2022 Organization Vasyl Stefanyk Precarpathian National University popup.description2  Keywords: analytic functions on Banach space, symmetric analytic functions of bounded type, algebras of analytic functions, spectrum of commutative algebra. Object of research: algebras of analytic functions in Banach space, spectra. The aim of the project is to describe the spectrum, analytical and algebraic structures on the spectrum for algebras of whole analytical functions of bounded type on a complex Banach space, in particular, symmetric analytical functions with respect to certain symmetry groups. Research methodology. Methods of the theory of analytic functions on Banach spaces (Aron-Berner continuation, properties of radius function), theory of symmetric analytic functions on spaces with symmetric structure (spaces with unconditional basis and permutable invariant spaces), methods of topological tensor products are used to solve the set problems, methods of the theory of linear and nonlinear operators on Banach spaces, methods of combinatorics and the theory of topological algebras. Results and their novelty. Using these approaches, algebraic and topological structures on the spectra of different algebras of analytic functions of bounded type on complex Banach spaces are described. In many cases, algebraic bases are found in such algebras. All results are new and published in the ranking of international mathematical journals. Product Description popup.authors Artemovych Orest D Vasylyshyn Taras Vasylovych Gavrylkiv Volodymyr Mykhaylovych Halushchak Svitlana Ihorivna Holubchak Oleh Mykhailovych Dmytryshyn Roman Ivanovych Zatorsky Roman Andriyovuch Kopach Mykhaylo Ivanovych Kravtsiv Victoria V. Labachuk Oksana Vasylivna Mykytsei Oksana Yaroslavivna Popov Mykhailo M Pryimak Halyna Mykolaivna Filevych Petro V popup.nrat_date 2022-04-05 Close