Entire Analytic Functions of Unbounded Type on Banach Spaces and Their Lineability

In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type ca...

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Bibliographic Details
Published in:Axioms 2021-09, Vol.10 (3), p.150
Main Authors: Zagorodnyuk, Andriy, Hihliuk, Anna
Format: Article
Language:English
Subjects:
Algebra
Analytic functions
analytic functions on Banach spaces
Banach spaces
Entire functions
functions of unbounded type
Mathematical analysis
Polynomials
Subspaces
symmetric polynomials on Banach spaces
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Summary:In the paper we establish some conditions under which a given sequence of polynomials on a Banach space X supports entire functions of unbounded type, and construct some counter examples. We show that if X is an infinite dimensional Banach space, then the set of entire functions of unbounded type can be represented as a union of infinite dimensional linear subspaces (without the origin). Moreover, we show that for some cases, the set of entire functions of unbounded type generated by a given sequence of polynomials contains an infinite dimensional algebra (without the origin). Some applications for symmetric analytic functions on Banach spaces are obtained.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms10030150