Advanced Studies in Pure Mathematics

Remark on $C_0$-semigroups with scaling invariance

Yasunori Maekawa

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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.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 337-345

Dates
Received: 15 December 2011
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934231

Digital Object Identifier
doi:10.2969/aspm/06410337

Mathematical Reviews number (MathSciNet)
MR3381220

Zentralblatt MATH identifier
1357.47043

Subjects
Primary: 47D03: Groups and semigroups of linear operators {For nonlinear operators, see 47H20; see also 20M20} 47D06: One-parameter semigroups and linear evolution equations [See also 34G10, 34K30]

Keywords
$C_0$-semigroups scaling and translation invariance

Citation

Maekawa, Yasunori. Remark on $C_0$-semigroups with scaling invariance. Nonlinear Dynamics in Partial Differential Equations, 337--345, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410337. https://projecteuclid.org/euclid.aspm/1540934231


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