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Is every absolutely convergent series convergent?
The Mathematical Gazette, 1977There are various ways of introducing a discussion of the completeness of the system of real numbers. In this article we take the unusual approach suggested by the provocative question of the title. In any elementary treatment of the convergence of sequences and series, a discussion of series of positive and negative terms will lead ...
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Non-absolutely Convergent Generalized Laplacian
Potential Analysis, 2020The authors introduce a generalization of the Laplace operator, based on a new type of non-absolutely convergent integral. With this tool, the authors prove new Blaschke-Privaloff-type criteria for harmonicity and superharmonicity. Moreover, such integral, where the integrand may be a highly oscillating pointwise function or a distribution-valued ...
Jan Malý, Ivan Netuka
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On the absolute convergence of multiple fourier series
Acta Mathematica Hungarica, 2007Let \(f:\mathbb R^N\to \mathbb C\) be a periodic function with period \(2\pi\) in each variable. The authors obtain sufficient conditions for the absolute convergence of the multiple Fourier series of the function \(f\) in terms of moduli of continuity, of bounded variation in the sense of Vitali or Hardy and Krause, and of the mixed partial derivative
Móricz, Ferenc, Veres, Antal
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Absolutely convergent expansions
Rendiconti del Circolo Matematico di Palermo, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Integral Operators and Absolute Convergence Systems
Siberian Mathematical Journal, 2002The author uses special integral operators (Carleman operators) to establish several special properties of absolute convergence systems for \(l_2\). The following notion of an absolute convergence system is used: a sequence \(\{g_n\}\subset M\) (\(M = M(X,\mu)\) denotes the space of all \(\mu\)-measurable \(\mu\)-a.e. finite functions on \(X\), where \(
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On absolute convergence of Vilenkin Fourier series
The science reports of the Kanazawa University＝金沢大学理科報告, 1987Let G be a Vilenkin group. That is, G is a compact, metrizable, zero- dimensional abelian group. Then X (dual of G) is a discrete, countable torsion group. There exists an increasing sequence \(\{X_ k\}^{\infty}_{k=0}\) of finite subgroups of X and a sequence \(\{\phi_ k\}^{\infty}_{k=0}\) of characters in X such that (i) \(X_ 0=\{0\}\), (ii) \(X_ k/X_{
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Absolute convergence of Vilenkin Fourier series
The science reports of the Kanazawa University＝金沢大学理科報告, 1984We give a theorem on the absolute convergence of Vilenkin Fourier series by using the notion of \(\lambda\)-bounded p-fluctuation.
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The Absolute Convergence of Series of Integrals
Proceedings of the London Mathematical Society, 1939Bosanquet, L. S., Kestelman, H.
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Absolute convergence factors of Lipschitz class functions for general Fourier series
Georgian Mathematical Journal, 2021Vakhtang Tsagareishvili
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