Relatively bounded extensions of generator perturbations

Horst Thieme, Jürgen Voigt

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The Miyadera perturbation theorem provides as a by-product that operators defined on a core for the generator of a Co-semigroup and satisfying the Miyadera condition have a relatively bounded extension to the domain of the generator. We show that a weakening of the Miyadera condition characterizes relative boundedness with respect to the generator. We also investigate extensions of these results to Hille-Yosida operators. The various conditions we use in the abstract part are illustrated by several examples.

Original languageEnglish (US)
Pages (from-to)947-969
Number of pages23
JournalRocky Mountain Journal of Mathematics
Issue number3
StatePublished - 2009


  • Hille-Yosida operator
  • Miyadera perturbation
  • Perturbation theory
  • Positive perturbation
  • Relative bound
  • Strongly continuous semigroup

ASJC Scopus subject areas

  • Mathematics(all)


Dive into the research topics of 'Relatively bounded extensions of generator perturbations'. Together they form a unique fingerprint.

Cite this