A note on functions which operate

Alan G. Konheim, Benjamin Weiss

Research output: Contribution to journalArticlepeer-review

Abstract

Let 𝐅, B denote two families of functions a, b: X → Y. A function F:Z ⊆Y → Y is said to operate in (𝐅, B) provided that for each a ∈𝐅 with range (a)⊆ Z we have F(a)∈ B. Let G denote a locally compact Abelian group. In this paper we characterize the functions which operate in two cases: (i) 𝐅 = ϕr(G) = positive definite functions on G with ϕ(e) = r and B = ϕi.d.,.(G) = infinitely divisible positive definite functions on G with ϕ(e) = s. (ii) 𝐅 = B = ϕ(G) = ϕi.d.,.(G).

Original languageEnglish
Pages (from-to)297-302
Number of pages6
JournalPacific Journal of Mathematics
Volume24
Issue number2
DOIs
StatePublished - Feb 1968
Externally publishedYes

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