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Information × Registration Number 0219U100474, 0116U003562 , R & D reports Title The research of analytical structures in the spectrum of holomorphic functions algebras on Banach space and in the inverse spectral problems popup.stage_title Head Zahorodniuk Andrii V., Доктор фізико-математичних наук Registration Date 13-02-2019 Organization SHEE "Precarpathian National University named after Vasyl Stefanyk" popup.description2 The purpose and tasks for which the project was directed. The project is aimed at studying the structures of an analytic variety on the spectra of different algebras of holomorphic (analytic) and infinitely smooth functions of the Banach space, including algebras of symmetric analytic functions on spaces with symmetric structure and algebras containing functions of unbounded type; study of homomorphisms of these algebras, differentiations, functional calculus with values ​​in these algebras; A description of the analytic dependencies of the Sturm-Liouville operator potential for a case where the potential is a generalized function of a certain class of Soblet and the Dirac operator is integrable in a square potential from spectral data. The object of the study is the algebra of entire functions of finite type on a complex Banach space, the subalgebra of entire functions of the Banach space, which include functions of unbounded type, algebras of symmetric analytic functions on Banach spaces with a symmetric basis, and invariant transformed spaces, algebras of infinitely differentiated (in real sense) of Banach space functions, spectra of these algebras, solutions of inverse spectral problems for Sturm-Liouville operators and Dirac operators. The subject of research is the structure of an analytic (smooth) variety on the spectra of the above algebras, the functional calculations in these algebras, the analytic dependence of the parameters of spectral problems on the spectra and spectral data of the corresponding operators Product Description popup.authors popup.nrat_date 2020-04-02 Close