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Information × Registration Number 0218U000424, 0115U002305 , R & D reports Title Homomorphisms and functional calculus algebra of analytic functions on Banach spaces popup.stage_title Head Zagorodnyuk Andriy Vasylyovych, Registration Date 29-01-2018 Organization SHEE "Ргесаграthiаn NаtionаІ Vаsyl Stеfаnік Univetrsity" popup.description2 In this paper, the homomorphisms of algebras of entire functions of bounded type on Banach spaces into commutative Banach algebra are investigated. The structure of the set of maximal ideals of algebras of R-analytic functions of a Banach space is established. A generalization of the extension of Arens for Banach algebras is described, and conditions for the continuity of algebraic operations on these sequences are established. The structure of the predicate algebra to Hb (A), where A is a certain Banach algebra, is described. A functional calculus is constructed in the algebras H_b (X) and W (X), and the theory of generalized functions from an infinite number of variables is developed with the use of the main functions of the subalgebra in H_b (X) and W (X). A functional calculus for a cumulative system of generators of compression of strongly continuous semigroups is constructed. A functional calculus is constructed in the spaces of generalized functions associated with analytic and R-analytic functions of the Banach space. The differentiation and homomorphisms in the algebras of analytic and R-analytic functions of the Banach space are investigated. Differentiation in abstract rings, in particular, in commutative rings, was also investigated. An operator calculus over a symmetric Fock space is constructed for a countable set of non-commutative generators of strongly continuous groups acting on the Hilbert space. The algebras of analytic functions on a complex Banach space that are invariant with respect to the action of a certain set of operators acting on a given space are investigated. Such invariant functions are called symmetric. The cases of Banach spaces of the type L_p and L_p for different groups of symmetry are considered. The spectra of such algebras and analytic structures on these spectra are described. In particular, the spectrum of the algebra of symmetric functions of bounded type on the spaces L_infty [a, b], L_infty [0, + infty] L_1 [0, +infty] and the factor-topology on this spectrum are described. Product Description popup.authors Іващук Наталія Леонідівна Артемович Орест Дем'янович Лопушанський Андрій Олегович popup.nrat_date 2020-04-02 Close