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This article is cited in 1 scientific paper (total in 1 paper)
The arithmetic of the characteristic Pólya functions
A. I. Il'inskii Kharkov State University
Abstract:
In the framework of the theory of D. Kendall's delphic semigroups are considered problems of divisibility in the semigroup pgr of convex characteristic functions on the semiaxis $(0,\infty)$. $N(\pi)=\{\varphi\in\pi:\varphi_1\mid\varphi\Rightarrow\varphi_1\equiv1\text{ or }\varphi_1=\varphi\}$ and $I_0(\pi)=\{\varphi\in\pi:\varphi_1\mid\varphi\Rightarrow\varphi_1\notin N(\pi)\}$. The following results are proved: 1) The semigroup pgr is almost delphic in the sense of R. Davidson. 2) $N(\pi)$ is a set of the type $G_\delta$ which is dense in $\pi$ (in the topology of uniform convergence on compacta). 3) The class $I_0(\pi)$ contains only the function identically equal to one.
Received: 01.04.1974
Citation:
A. I. Il'inskii, “The arithmetic of the characteristic Pólya functions”, Mat. Zametki, 21:5 (1977), 717–725; Math. Notes, 21:5 (1977), 400–405
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https://www.mathnet.ru/eng/mzm8002 https://www.mathnet.ru/eng/mzm/v21/i5/p717
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