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Registration Number

0221U105887, 0121U111037 , R & D reports

Title

Symmetries in algebraic and topological structures on infinitely dimensional analytic manifolds and their possible applications

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Head

Zagorodnyuk Andriy V., Кандидат фізико-математичних наук

Registration Date

07-09-2021

Organization

Vasyl Stefanyk Precarpathian National University, State Higher Educational Institution

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 Report SRW: 67p., there are 8 chapters. Research object – infinite-dimensional manifolds, symmetric mappings. The goal of the project is to establish the properties of spectra (and their subsets) of algebras of S-invariant analytic functions of bounded type on a Banach space X for different semigroups of symmetry S and spaces X. Also, the case of algebras of real analytic functions on real Banach spaces will be considered. In addition, the results obtained for the algebras of analytic functions in Banach space generated by a countable family of polynomials will be generalized. Research methodology: The algebra of analytic functions on a complex Banach space invariant with respect to some group or semigroup of operators, in many interesting cases, has a countable algebraic basis of homogeneous polynomials. This fact is useful because each complex homomorphism (an element of the spectrum of this algebra) can be completely determined by its values on polynomials from this basis. Thus, we can obtain an image of the spectrum in the form of some subset of sequence space. The next step in the research is to study block symmetric and block supersymmetric algebras. That is, a semigroup of symmetry will act by rearranging individual blocks (finite-dimensional subspaces). Results and novelty: We received the complete description of structures of spectra of algebras of block-symmetric analytic functions of bounded type on L∞ and algebraic bases for sequence spaces. We found representations of spectra of algebras of block-symmetric analytic functions on L∞ in the form of an analytic manifold and a representation of the Gelfand transform in this algebra. The case of block-symmetric *-analytic functions on L∞ are consider. In particular, to investigate the completion of this algebra in the uniform topology. We found conditions of approximation of continuous symmetric functions by *-analytic functions. We found algebraic bases of block-symmetric analytic functions.

Product Description

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Bandura Andrii I.
Burtniak Ivan V
Vasylyshyn Taras Vasylovych
Halushchak Svitlana I.
Hladkyi Volodymyr Yaroslavovych
Labachuk Oksana Vasylivna
Martsinkiv Mariia Volodymyrivna
Novosad Zoriana G
Cherneha Iryna V.

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2021-09-07