Convergence at the origin of integrated semigroups

• Autorzy: Vincent Cachia
• Języki publikacji: EN

Abstrakty

EN

We study a classification of κ-times integrated semigroups (for κ > 0) by their (uniform) rate of convergence at the origin: $||S(t)|| = 𝒪(t^{α})$ as t → 0 (0 ≤ α ≤ κ). By an improved generation theorem we characterize this behaviour by Hille-Yosida type estimates. Then we consider integrated semigroups with holomorphic extension and characterize their convergence at the origin, as well as the existence of boundary values, by estimates of the associated holomorphic semigroup. Various examples illustrate these results. The particular case α = κ, which corresponds to the notions of Riesz means or tempered integrated semigroups, is of special interest; as an application, it leads to an integrated version of Euler's exponential formula.

Kategorie tematyczne

• 47D03: Groups and semigroups of linear operators
• 47D62: Integrated semigroups

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2008
• Tom: 187
• Numer: 3
• Strony: 199-218

Daty

wydano

2008

Twórcy

autor

Vincent Cachia

• Department of Theoretical Physics, University of Geneva, quai Ernest-Ansermet 24, CH-1211 Genève 4, Switzerland

Identyfikatory

DOI

10.4064/sm187-3-1