Radius of analyticity of analytic functions on Banach spaces

Christopher Boyd; Raymond A. Ryan; Nina Snigireva

doi:10.1016/j.jmaa.2018.03.004

Radius of analyticity of analytic functions on Banach spaces

Christopher Boyd, Raymond A. Ryan, Nina Snigireva

Mathematics

University College Dublin

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

2 Citations (Scopus)

Abstract

We examine the question of when the radius of analyticity of a real analytic function on a real Banach space is equal to its radius of uniform convergence. We will see that a positive solution to this problem on ℓ₁ implies a positive solution on all Banach spaces. In the final section we show that our question has an affirmative answer for power series of positive polynomials on Banach lattices.

Original language	English
Pages (from-to)	40-49
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	463
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.03.004
Publication status	Published - 1 Jul 2018

Keywords

Banach lattice
Radius of convergence
Real analytic function
Regular polynomial

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10.1016/j.jmaa.2018.03.004

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abstract = "We examine the question of when the radius of analyticity of a real analytic function on a real Banach space is equal to its radius of uniform convergence. We will see that a positive solution to this problem on ℓ1 implies a positive solution on all Banach spaces. In the final section we show that our question has an affirmative answer for power series of positive polynomials on Banach lattices.",

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AU - Snigireva, Nina

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AB - We examine the question of when the radius of analyticity of a real analytic function on a real Banach space is equal to its radius of uniform convergence. We will see that a positive solution to this problem on ℓ1 implies a positive solution on all Banach spaces. In the final section we show that our question has an affirmative answer for power series of positive polynomials on Banach lattices.

KW - Banach lattice

KW - Radius of convergence

KW - Real analytic function

KW - Regular polynomial

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DO - 10.1016/j.jmaa.2018.03.004

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JF - Journal of Mathematical Analysis and Applications

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Radius of analyticity of analytic functions on Banach spaces

Abstract

Keywords

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