A two-parameter extension of Urbanik’s product convolution semigroup
A two-parameter extension of Urbanik’s product convolution semigroup
We prove that s_n(a,b)=\Gamma(an+b)/\Gamma(b), n=0,1,\ldots is an infinitely divisible Stieltjes moment sequence for arbitrary a,b>0. Its powers s_n(a,b)^c, c>0 are Stieltjes determinate if and only if ac\le 2. The latter was conjectured in a paper by Lin (ArXiv: 1711.01536) in the case b=1. We describe a product convolution semigroup \tau_c(a,b), …