Refined scales of decaying rates of operator semigroups on Hilbert spaces: typical behaviour

2018/04/20 by Moacir Aloisio, Aloisio, Moacir, Silas L. Carvalho +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1804.07838

openalex publication_date 2018/04/20 · openalex created_date 2018/05/07 · openalex updated_date 2026/07/28

Abstract

We study relations between the decaying rates of operator semigroups on Hilbert spaces and some spectral properties of their respective generators; in particular, we show that the decaying rates of orbits of semigroups which are stable but not exponentially stable, typically in Baire's sense, depend on sequences of time going to infinity.

Citations

• On the spectrum of 𝐶₀-semigroups
• Optimal polynomial decay of functions and operator semigroups

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