Exponential convergence of Markovian semigroups and their spectra on L p-spaces

Seiichiro Kusuoka, Ichiro Shigekawa

Research output: Contribution to journalArticle

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Abstract

Markovian semigroups on L2-space with suitable conditions can be regarded as Markovian semigroups on Lp-spaces for p ∈ [1,∞). When we additionally assume the ergodicity of the Markovian semigroups, the rate of convergence on Lp-space for each p is considerable. However, the rate of convergence depends on the norm of the space. The purpose of this paper is to investigate the relation between the rates on Lp-spaces for different p,s, to obtain some sufficient condition for the rates to be independent of p, and to give an example for which the rates depend on p.We also consider spectra of Markovian semigroups on L p-spaces, because the rate of convergence is closely related to the spectra.

Original languageEnglish
Pages (from-to)367-399
Number of pages33
JournalKyoto Journal of Mathematics
Volume54
Issue number2
DOIs
Publication statusPublished - 2014
Externally publishedYes

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L-p space
Exponential Convergence
Lp Spaces
Semigroup
Rate of Convergence
Ergodicity
Norm
Sufficient Conditions

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Exponential convergence of Markovian semigroups and their spectra on L p-spaces. / Kusuoka, Seiichiro; Shigekawa, Ichiro.

In: Kyoto Journal of Mathematics, Vol. 54, No. 2, 2014, p. 367-399.

Research output: Contribution to journalArticle

Kusuoka, Seiichiro ; Shigekawa, Ichiro. / Exponential convergence of Markovian semigroups and their spectra on L p-spaces. In: Kyoto Journal of Mathematics. 2014 ; Vol. 54, No. 2. pp. 367-399.
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