Universal extrapolation spaces for C0-semigroups

Sven Ake Wegner

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

The classical theory of Sobolev towers allows for the construction of an infinite ascending chain of extrapolation spaces and an infinite descending chain of interpolation spaces associated with a given C0-semigroup on a Banach space. In this note we first generalize the latter to the case of a strongly continuous and exponentially equicontinuous semigroup on a complete locally convex space. As a new concept—even for C0-semigroups on Banach spaces—we then define a universal extrapolation space as the completion of the inductive limit of the ascending chain. Under mild assumptions we show that the semigroup extends to this space and that it is generated by an automorphism of the latter. Dually, we define a universal interpolation space as the projective limit of the descending chain. We show that the restriction of the initial semigroup to this space is again a semigroup and always has an automorphism as generator.

Original languageEnglish
Pages (from-to)447-463
Number of pages17
JournalAnnali dell'Universita di Ferrara
Volume60
Issue number2
DOIs
Publication statusPublished - Nov 2014

Keywords

  • Extrapolation space
  • Interpolation space
  • Semigroup
  • Sobolev tower

ASJC Scopus subject areas

  • Mathematics(all)

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