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Multipliers of Absolute Convergence
Mathematical Notes, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tsagareishvili, V. Sh. +1 more
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A variation on absolutely almost convergence
AIP Conference Proceedings, 2018International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) -- SEP 25-30, 2017 -- Thessaloniki ...
Cakalli, Huseyin, Taylan, Iffet
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On the Absolute Convergence of Dirichlet Series
The Annals of Mathematics, 1931This paper contains a complete solution of a problem of great importance for the theory of Dirichlet series, which was formulated by \textit{H. Bohr} [Nachr. Ges. Wiss. Göttingen, Math.-Phys. Kl. 1913, 441--488 (1913; JFM 44.0306.01)] but during 18 years resisted the efforts of several mathematicians.
Bohnenblust, H. F., Hille, Einar
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Absolute Convergence in Ordered Fields
The American Mathematical Monthly, 2014We explore the distinction between convergence and absolute convergence of se- ries in both Archimedean and non-Archimedean ordered fields and find that the relationship between them is closely connected to sequential (Cauchy) completeness.
Pete L. Clark, Niels J. Diepeveen
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ON SETS OF ABSOLUTE CONVERGENCE
Mathematics of the USSR-Sbornik, 1981In this paper the author indicates a certain class of planar curves such that any set of positive linear measure on them is a set of absolute convergence for double trigonometric series. Bibliography: 11 titles.
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Convergence, Absolute Convergence and Strong Convergence with Periodicity
Journal of the London Mathematical Society, 1973We write \(| S|\in Z_k\), where \(k\) \((\geq 1)\) is a positive integer, if the series \(\sum_{n=0}^\infty (S_{n+k}-S_n)\) converges, and call \(Z_k\) the space of all convergent sequences of period \(k\). Here several theorems have been proved, connecting the \(Z_k\), \(| Z_k|\), \(C_\alpha\), \(| C_\alpha|\) etc. Following are the first two theorems
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Series that Converge Absolutely but Don't Converge
The College Mathematics Journal, 2012If a series of real numbers converges absolutely, then it converges. The usual proof requires completeness in the form of the Cauchy criterion. Failing completeness, the result is false.
Robert Kantrowitz, Michael Schramm
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ABSOLUTE CONVERGENCE OF LACUNARY SERIES
Mathematics of the USSR-Izvestiya, 1967Zygmund's theorem on absolute convergence of lacunary trigonometric series is generalized to apply to a wider class of lacunary sequences. An analogous result is established for the Walsh system.
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Absolute Almost Convergence and Riesz Convergence
2014In this chapter, we define the notion of almost bounded variation and absolute almost convergence for double sequences. We use the definition of absolute almost convergence to define absolute almost conservative and absolute almost regular matrices and find necessary and sufficient conditions to characterize these matrices.
M. Mursaleen, S. A. Mohiuddine
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Convergence as a Cue to Absolute Distance
The Journal of Psychology, 1961(1961). Convergence as a Cue to Absolute Distance. The Journal of Psychology: Vol. 52, No. 2, pp. 287-301.
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