Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces
In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space <inline-formula><math display="inline"><semantics><mrow><mi>X</mi><mo>.</mo></mrow></semantics></math></inli...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-11-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/9/4/133 |
| _version_ | 1797547647761907712 |
|---|---|
| author | Andriy Zagorodnyuk Anna Hihliuk |
| author_facet | Andriy Zagorodnyuk Anna Hihliuk |
| author_sort | Andriy Zagorodnyuk |
| collection | DOAJ |
| description | In this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space <inline-formula><math display="inline"><semantics><mrow><mi>X</mi><mo>.</mo></mrow></semantics></math></inline-formula> The main question is: under which conditions is there an analytic function of unbounded type on <i>X</i> such that its Taylor polynomials are in prescribed subspaces of polynomials? We obtain some sufficient conditions for a function <i>f</i> to be of unbounded type and show that there are various subalgebras of polynomials that support analytic functions of unbounded type. In particular, some examples of symmetric analytic functions of unbounded type are constructed. |
| first_indexed | 2024-03-10T14:47:05Z |
| format | Article |
| id | doaj.art-b660fbb546e0482381fb704f3db4ffc3 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T14:47:05Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-b660fbb546e0482381fb704f3db4ffc32023-11-20T21:20:34ZengMDPI AGAxioms2075-16802020-11-019413310.3390/axioms9040133Classes of Entire Analytic Functions of Unbounded Type on Banach SpacesAndriy Zagorodnyuk0Anna Hihliuk1Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, UkraineFaculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenka Str., 76018 Ivano-Frankivsk, UkraineIn this paper we investigate analytic functions of unbounded type on a complex infinite dimensional Banach space <inline-formula><math display="inline"><semantics><mrow><mi>X</mi><mo>.</mo></mrow></semantics></math></inline-formula> The main question is: under which conditions is there an analytic function of unbounded type on <i>X</i> such that its Taylor polynomials are in prescribed subspaces of polynomials? We obtain some sufficient conditions for a function <i>f</i> to be of unbounded type and show that there are various subalgebras of polynomials that support analytic functions of unbounded type. In particular, some examples of symmetric analytic functions of unbounded type are constructed.https://www.mdpi.com/2075-1680/9/4/133analytic functions on Banach spacesfunctions of unbounded typesymmetric polynomials on Banach spaces |
| spellingShingle | Andriy Zagorodnyuk Anna Hihliuk Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces Axioms analytic functions on Banach spaces functions of unbounded type symmetric polynomials on Banach spaces |
| title | Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces |
| title_full | Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces |
| title_fullStr | Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces |
| title_full_unstemmed | Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces |
| title_short | Classes of Entire Analytic Functions of Unbounded Type on Banach Spaces |
| title_sort | classes of entire analytic functions of unbounded type on banach spaces |
| topic | analytic functions on Banach spaces functions of unbounded type symmetric polynomials on Banach spaces |
| url | https://www.mdpi.com/2075-1680/9/4/133 |
| work_keys_str_mv | AT andriyzagorodnyuk classesofentireanalyticfunctionsofunboundedtypeonbanachspaces AT annahihliuk classesofentireanalyticfunctionsofunboundedtypeonbanachspaces |