TY - JOUR
T1 - A note on functions which operate
AU - Konheim, Alan G.
AU - Weiss, Benjamin
PY - 1968/2
Y1 - 1968/2
N2 - 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).
AB - 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).
UR - http://www.scopus.com/inward/record.url?scp=84972534454&partnerID=8YFLogxK
U2 - 10.2140/pjm.1968.24.297
DO - 10.2140/pjm.1968.24.297
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AN - SCOPUS:84972534454
SN - 0030-8730
VL - 24
SP - 297
EP - 302
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
IS - 2
ER -