This paper grew out of discussions with S. Bochner.It would be hard now to disengage his contributions from mine.We shall characterize those families (pt)o ,/• (r)-/(r)] t t(2) = af (r) + bf"(r) + J [f(r + *)-f(r) -^-jG(d f as / decreases to 0. Thus (St) has an infinitesimal generator; one would expect it to have an expression like (2).
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G. A. Hunt (1956) studied this question.
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