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Mat. Zametki, 1977, Volume 21, Issue 5, Pages 717–725 (Mi mz8002)  

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 $(0,\infty)$. $N(\pi)=\{\varphi\in\pi:\varphi_1\mid\varphi\Rightarrow\varphi_1\equiv1 or \varphi_1=\varphi\}$ 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.

Full text: PDF file (737 kB)

English version:
Mathematical Notes, 1977, 21:5, 400–405

Bibliographic databases:

UDC: 519.2
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

Citation in format AMSBIB
\Bibitem{Ili77}
\by A.~I.~Il'inskii
\paper The arithmetic of the characteristic P\'olya functions
\jour Mat. Zametki
\yr 1977
\vol 21
\issue 5
\pages 717--725
\mathnet{http://mi.mathnet.ru/mz8002}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=451341}
\zmath{https://zbmath.org/?q=an:0401.60006|0369.60016}
\transl
\jour Math. Notes
\yr 1977
\vol 21
\issue 5
\pages 400--405
\crossref{https://doi.org/10.1007/BF01788238}


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