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Volume 6, Issue 1, 1 April 2024, Pages 13-29
Abstract. The paper is devoted to two problems pivotal in the generation theory. The first concerns verifying whether a normalized holomorphic function is an infinitesimal generator. It is also important to trace the influence of properties of a generator on the dynamic behavior of the generated semigroup. Recently, these problems have been studied using the so-called filtrations of generators. In this paper we study three filtrations.The study of the first began earlier, the second is a new one, while the third consists of functions studied previously with no connection to complex dynamics. For all filtration classes studied in the paper, dynamic properties of the corresponding semigroups are established and estimates for the Fekete-Szegö functional are given.
How to Cite this Article:
M. Elin, F. Jacobzon, D. Shoikhet, Filtration families of semigroup generators. The Fekete-Szegö problem, Appl. Set-Valued Anal. Optim. 6 (2024), 13-29.