Refined decay rates of C₀-semigroups on Banach spaces

2023/11/09 by Genilson Santana, de Santana, Genilson S., Silas L. Carvalho +1
Computer Science · Engineering · Mathematics · #34D05 #42B15 #47D06 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2311.05121

openalex publication_date 2023/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study rates of decay for C₀-semigroups on Banach spaces under the assumption that the norm of the resolvent of the semigroup generator grows with \vert s\vert^βlog(\vert s\vert)^b, β, b ≥ 0, as \vert s\vert→∞, and with \vert s\vert^-αlog(1/\vert s\vert)^a, α, a ≥ 0, as \vert s\vert → 0. Our results do not suppose that the semigroup is bounded. In particular, for a=b=0, our results improve the rates involving Fourier types obtained by Rozendaal and Veraar (J. Funct. Anal. 275(10): 2845-2894, 2018).

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