The non-analytic growth bound of a C-0-semigroup and inhomogeneous Cauchy problems

Journal article

The non-analytic growth bound ζ(T) of a C0-semigroup T measures the extent to which T can be approximated by a holomorphic function, and it is related to spectral properties of the generator A in regions of ℂ far from the real axis. We show that ζ(T) can be characterised by means of Fourier multiplier properties of the resolvent of A far from the real axis, and also by existence and uniqueness of mild solutions of inhomogeneous Cauchy problems of the form u′(t) = Au(t) + f(t) on ℝ where the Carleman spectra of f and u are far from the origin. The corresponding results for the exponential growth bound ω0(T) have been established earlier by other authors. © 2003 Elsevier Inc. All rights reserved.

Authors: Batty, C; Srivastava, S

• Publication status: Published
• Journal: JOURNAL OF DIFFERENTIAL EQUATIONS
• Volume: 194
• Issue: 2
• Pages: 300-327
• Publication date: 2003-11-01
• DOI: 10.1016/S0022-0396(03)00195-5
• ISSN: 0022-0396
• Language: English
• Keywords: semigroup; regularly admissible; Fourier multiplier; non-analytic; growth bound; inhomogeneous Cauchy problem; non-resonance; resolvent; Carleman spectrum