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 Mat. Zametki: Year: Volume: Issue: Page: Find

 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

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}