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