Entire curves having bounded l-index in ℓ∞
Journal Title: Математичні Студії - Year 2019, Vol 52, Issue 1
Abstract
In this paper we propose an approach to introduce a concept of bounded index in an infinite-dimensional space. Our object of investigation is the space ℓ∞ equipped with the norm ∥x∥∞=sup{|xn|:n∈N}. We consider entire curves from C to ℓ∞ and prove proposition indicating connection between of the l-index boundedness of every component of the curve and the l-index boundedness of the curve. Moreover, we obtain sufficient conditions of the l-index boundednes of entire curves in the space. They describe local behavior of norm of derivatives of the entire curves on the discs. Also, there is posed a problem on necessary conditions of the l-index boundedness of entire curves in infinite-dimensional spaces.
Authors and Affiliations
Andriy Bandura
Keywords
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- EP ID EP673833
- DOI 10.30970/ms.52.1.108-112
- Views 59
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