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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2020-11-01
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| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/9/4/133 |
| Summary: | 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. |
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| ISSN: | 2075-1680 |