Vasylyshyn S. Algebras of analytic functions on Banach spaces generated by a countable set of generating elements.

Українська версія

Thesis for the degree of Doctor of Philosophy (PhD)

State registration number

0823U101625

Thesis Registration Form

0823U101625.pdf

Applicant for

Specialization

  • 111 - Математика

Specialized Academic Board

ДФ 20.051.089

Vasyl Stefanyk Precarpathian National University

Essay

The thesis is fulfilled within the theory of analytic functions on Banach spaces. The object of the research is algebras of entire functions generated by countable sets of algebraically independent polynomials on complex Banach spaces and spectra of such algebras. The purpose of the research is to study the properties of algebras of entire functions generated by countable sets of algebraically independent polynomials on complex Banach spaces. Research methods. In the thesis the methods of mathematical analysis, infinite-dimensional complex analysis, theory of analytic functions, and the theory of the Fréchet algebras were used. The obtained results and their scientific novelty. In the thesis, the following results were obtained for the first time: the spectra of some countably generated algebras on complex Banach spaces of sequences were investigated; conditions under which such algebras are isomorphic were established; algebraic bases in countably generated algebras of polynomials were studied. Application field. The thesis has a theoretical nature. Its results can be used in the theory of polynomials on Banach spaces, theory of analytic functions on Banach spaces, and the theory of the Fréchet algebras.

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Research papers

1. Halushchak S. I. Spectra of some algebras of entire functions of bounded type, generated by a sequence of polynomials // Carpathian Math. Publ. // категорія А. — 2019. — Vol. 11, № 2. — P. 311 - 320. DOI: https://doi.org/10.15330/cmp.11.2.311-320 URL: https://www.scopus.com/record/display.uri?eid=2-s2.0-85078306604&origin=resultslist

2. Halushchak S. I. Isomorphisms of some algebras of analytic functions of bounded type on Banach spaces // Mat. Stud. // категорія А. — 2021. — Vol. 56, Iss. 1. — P. 107 - 112. DOI: https://doi.org/10.30970/ms.56.1.107-112 URL: https://www.scopus.com/record/display.uri?eid=2-s2.0-85120080599&origin=resultslist

3. Halushchak S. Algebras of analytic functions on Banach spaces, generated by countable sets of polynomials and their properties // AIP Conference Proceedings — 2022. — Vol. 2483, Article Number 030006. DOI: https://doi.org/10.1063/5.0117601 URL: https://www.scopus.com/record/display.uri?eid=2-s2.0-85142505934&origin=resultslist

4. Vasylyshyn S. I. Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces and operations on spectra // Carpathian Math. Publ. // категорія А. — 2023. — Vol. 15, № 1. — P. 104 -119. DOI: https://doi.org/10.15330/cmp.15.1.104-119 URL: https://www.scopus.com/record/display.uri?eid=2-s2.0-85163657874&origin=resultslist

5. Novosad Z., Vasylyshyn S., Zagorodnyuk A. Countably generated algebras of analytic functions on Banach spaces // Axioms. — 2023. — Vol. 12, Iss. 8. — Article Number 798, 21 p. DOI: https://doi.org/10.3390/axioms12080798 URL: https://www.scopus.com/record/display.uri?eid=2-s2.0-85169106693&origin=resultslist

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