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On Almost convergence on the real line and its application to bounded analytic functions | | Ryoichi Kunisada
; | | Date: |
4 Jan 2023 | | Abstract: | We address the study of topologically invariant means and almost convergence
on the real numbers $mathbb{R}$. Here, the former is a certain class of
invariant means on $L^{infty}(mathbb{R})$ and the latter is a summability
method defined by them. Almost convergence on $mathbb{R}$ was firstly
introduced by Raimi (1957) as a generalization of Lorentz’s almost convergence
for bounded sequences. We extensively generalize his result of analytic
characterization of almost convergence and explore its application to the
theory of Hardy space. Specifically, we establish the relation between the
asymptotic behavior on the imaginary axis and that at infinity of bounded
analytic functions defined on the right half plane. | | Source: | arXiv, 2301.01629 | | Services: | Forum | Review | PDF | Favorites | |
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