Lpspectra of pseudodifferential operators generating integrated semigroups

Matthias Georg Hieber

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Consider the Lp-realization Opp(a) of a pseudodifferential operator with symbol a ϵsm p, 0having constant coefficients. We show that for a certain class of symbols the spectrum of Opp(a) is independent of p. This implies that Opp(a) generates an TV-times integrated semigroup on W(W) for a certain N if and only if pOpp(a)≠ ∅ and the numerical range of a is contained in a left half-plane. Our method allows us also to construct examples of operators generating integrated semigroups on Lp(Rn) if and only if p is sufficiently close to 2.

Original languageEnglish
Pages (from-to)4023-4035
Number of pages13
JournalTransactions of the American Mathematical Society
Volume347
Issue number10
DOIs
Publication statusPublished - 1995
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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