Remark on $C_0$-semigroups with scaling invariance

Maekawa, Yasunori

doi:10.2969/aspm/06410337

VOL. 64 | 2015 Remark on $C_0$-semigroups with scaling invariance

Yasunori Maekawa

Editor(s) Shin-Ichiro Ei, Shuichi Kawashima, Masato Kimura, Tetsu Mizumachi

Adv. Stud. Pure Math., 2015: 337-345 (2015) DOI: 10.2969/aspm/06410337

Abstract

We study $C_0$-semigroups acting on a Banach space which possess an invariant property with respect to an action of the multiplicative group of positive real numbers (scaling). Some properties on the domains or the spectrum of the associated generators are presented.