Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra
We consider the subalgebra of the Fréchet algebra of entire functions of bounded type, generated by a countable set of algebraically independent homogeneous polynomials on the complex Banach space $X.$ We investigate the spectrum of this subalgebra in the case $X = \ell_1.$ We also consider some shi...
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2023-06-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
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| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/6800 |
| _version_ | 1797205777844273152 |
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| author | S.I. Vasylyshyn |
| author_facet | S.I. Vasylyshyn |
| author_sort | S.I. Vasylyshyn |
| collection | DOAJ |
| description | We consider the subalgebra of the Fréchet algebra of entire functions of bounded type, generated by a countable set of algebraically independent homogeneous polynomials on the complex Banach space $X.$ We investigate the spectrum of this subalgebra in the case $X = \ell_1.$ We also consider some shift type operations that can be performed on the spectrum of this subalgebra in the case $X = \ell_p$ with $p \geq 1$. |
| first_indexed | 2024-04-24T08:56:31Z |
| format | Article |
| id | doaj.art-0ab71fa5314f4e4591f9e1dd7486d53b |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-04-24T08:56:31Z |
| publishDate | 2023-06-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-0ab71fa5314f4e4591f9e1dd7486d53b2024-04-16T07:13:58ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102023-06-0115110411910.15330/cmp.15.1.104-1195920Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectraS.I. Vasylyshyn0Vasyl Stefanyk Precarpathian National University, 57 Shevchenka str., 76018, Ivano-Frankivsk, UkraineWe consider the subalgebra of the Fréchet algebra of entire functions of bounded type, generated by a countable set of algebraically independent homogeneous polynomials on the complex Banach space $X.$ We investigate the spectrum of this subalgebra in the case $X = \ell_1.$ We also consider some shift type operations that can be performed on the spectrum of this subalgebra in the case $X = \ell_p$ with $p \geq 1$.https://journals.pnu.edu.ua/index.php/cmp/article/view/6800$n$-homogeneous polynomialanalytic functionspectrum of an algebra |
| spellingShingle | S.I. Vasylyshyn Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra Karpatsʹkì Matematičnì Publìkacìï $n$-homogeneous polynomial analytic function spectrum of an algebra |
| title | Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra |
| title_full | Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra |
| title_fullStr | Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra |
| title_full_unstemmed | Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra |
| title_short | Spectra of algebras of analytic functions, generated by sequences of polynomials on Banach spaces, and operations on spectra |
| title_sort | spectra of algebras of analytic functions generated by sequences of polynomials on banach spaces and operations on spectra |
| topic | $n$-homogeneous polynomial analytic function spectrum of an algebra |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/6800 |
| work_keys_str_mv | AT sivasylyshyn spectraofalgebrasofanalyticfunctionsgeneratedbysequencesofpolynomialsonbanachspacesandoperationsonspectra |