Abstract
In the framework of the theory of D. Kendall's delphic semigroups are considered problems of divisibility in the semigroup π of convex characteristic functions on the semiaxis (0,∞). Letn (π)={ϕεπ:ϕ1¦ϕ⇒ϕ1≡1 or ϕ1=ϕ}, and Io(π)={ϕεπ: ϕ1¦ϕ ⇒ϕ1 ∉N(π)}. The following results are proved: 1) The semigroup π is almost delphic in the sense of R. Davidson. 2) N(π) is a set of the type Gδ which is dense in π (in the topology of uniform convergence on compacta). 3) The class Io(π) contains only the function identically equal to one.
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Translated from Matematicheskie Zametki, Vol. 21, No. 5, pp. 717–725, May, 1977.
The author thanks I. V. Ostrovskii for the formulation of the problem and valuable remarks.
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Il'inskii, A.I. The arithmetic of the characteristic Pólya functions. Mathematical Notes of the Academy of Sciences of the USSR 21, 400–405 (1977). https://doi.org/10.1007/BF01788238
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DOI: https://doi.org/10.1007/BF01788238