We study the problem of characterizing membership of normalized holomorphic functions of the disc to the class of infinitesimal generators and their sectorial analytical extension. We provide new formulas and applications to dynamics of the corresponding semigroups using filtrations of the class of infinitesimal generators.
"Filtrations of infinitesimal generators." Funct. Approx. Comment. Math. 59 (1) 99 - 115, September 2018. https://doi.org/10.7169/facm/1710