Advances in operator theory 

About: Advances in operator theory is an academic journal published by Birkhäuser. The journal publishes majorly in the area(s): Chemistry & Computer science. It has an ISSN identifier of 2538-225X. Over the lifetime, 94 publications have been published receiving 47 citations.

Behavior of Kreiss bounded $$C_0$$-semigroups on a Hilbert space

Abstract: Abstract We prove that a Kreiss bounded $$C_0$$ C 0 semigroup $$(T_t)_{t \ge 0}$$ ( T t ) t ≥ 0 on a Hilbert space has asymptotics $$\left\| T_t\right\| = {\mathcal{O}}\big (t/\sqrt{\log (t)}\big ).$$ T t = O ( t / log ( t ) ) . Then, we give an application to perturbed wave equation.

Moment functions of higher rank on polynomial hypergroups

Abstract: In this paper we consider generalized moment functions of higher order. These functions are closely related to the well-known functions of binomial type which have been investigated on various abstract structures. In our former paper we investigated the properties of generalized moment functions of higher order on commutative groups. In particular, we proved the characterization of generalized moment functions on a commutative group as the product of an exponential and composition of multivariate Bell polynomial and a sequence additive functions. In the present paper we continue the study of generalized moment function sequences of higher order in the more abstract setting, namely we consider functions defined on a hypergroup. We characterize these functions on the polynomial hypergroup in one variable by means of partial derivatives of a composition of polynomials generating the polynomial hypergroup and an analytic function. As an example, we give an explicit formula for moment generating functions of rank at most two on the Tchebyshev hypergroup.