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Information × Registration Number 0212U004183, 0111U008858 , R & D reports Title Homomorphisms and differentiation in algebras of smooth and analytical functions on Banach spaces. popup.stage_title Head Zagorodnyuk A. V., Registration Date 31-01-2012 Organization Pidstryhach Institute of Applied Problems of Mechanics and Mathematics NAS of Ukraine popup.description2 Object of study: spectrum of algebras of analytic functions of the Banach space; functional calculus in algebra of analytic functions; automorphism and differentiation of different algebras of analytic and smooth functions on the Banach spaces; Hardy space of analytic functions of infinite number of variables. Objective of work: to describe the set of maximal ideals (spectrums) of algebras of smooth and analytic functions on complex Banach space and to construct analysis (differentiation, integration, analogue of generalized functions) on these spectrums. As a basic example we consider the algebras of analytic bounded-type functions on the infinite-dimension Banach space. The spectrums of this algebra are a linear space containing the initial Banach space and limited sets of it are relatively compact in Gelfand topology. On this space the functions from the given algebra and complexly conjugated functions continue on this space in a natural way. The algebras of continuous functions, differentiated functions, the measure spaces and spectrums of these algebras are studied. The differential and integral calculus on the spectrum is developed and sufficiently narrow classes of infinitely differentiated functions on the spectrum (the spaces of teste functions are selected), the spaces of generalized functions are constructed as conjugated to the spaces of test functions. The algebras of symmetric analytic functions on the spaces with symmetric basis and rearrangably invariant spaces and Banach algebras of bounded analytic functions in a sphere of the Banach space are studied similarly. Besides, the abstract Hardy spaces corresponding to these algebras are considered, the operations in these space are studied. Product Description popup.authors Боценюк О.М. Гринів Р.О. Загороднюк А.В. Лозинська В.Я. Митрофанов М.А. Равський О.В. Чернега І.В. Шарин С.В. popup.nrat_date 2020-04-02 Close