dc.contributor.author Mischler, Stéphane dc.date.accessioned 2017-12-01T10:25:08Z dc.date.available 2017-12-01T10:25:08Z dc.date.issued 2016 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/17136 dc.language.iso en en dc.subject growth-fragmentation equations dc.subject.ddc 515 en dc.title Erratum: Spectral analysis of semigroups and growth-fragmentation equations dc.type Document de travail / Working paper dc.description.abstracten We correct the article [S. Mischler, J. Scher, Spectral analysis of semigroups and growth-fragmentation equations. Ann. Inst. H. Poincar Anal. Non Linaire 33 (2016), no. 3, 849898]. In the article , there was an error in Step 1 in the proof of Theorem 2.1 that we were not able to fix, with fatal repercussions on most of the abstract spectral analysis results (Corollary 2.4, Theorem 3.1, Theorem 3.3 and Theorem 3.5 in ). However, we claim that Corollary 2.5 is correct and that we may slightly modify the statements of the other above mentioned abstract results in order to make them correct and then to use these variants in order to repair the proof of [2, Theorem 1.1]. We employ the notation and assumptions of , except that we replace assumption (H2) by the assumptions (h2) or (h2 ′) below. More precisely, we consider a Banach space X and the generator Λ of a strongly continuous semigroup S Λ on X. We assume that Λ splits as Λ = A + B where B is the generator of a strongly continuous semigroup S B and A is B-bounded. We also assume that the operators A and S B satisfy one of the two following regularizing properties of an iterated enough convolution product: (h2) there exist ζ ∈ (0, 1] and ζ ′ ∈ [0, ζ) such that A ∈ B(X ζ ′ , X) and there exists an integer n ≥ 1 such that for any a > a * , there holds ∀ t ≥ 0, (AS B) (* n) (t) B(X,X ζ) ≤ C a,n,ζ e at for a constant C a,n,ζ ∈ (0, ∞), or (h2 ′) there exist ζ ∈ [−1, 0) and ζ ′ ∈ (ζ, 0] such that A ∈ B(X, X ζ ′) and there exists an integer n ≥ 1 such that for any a > a * , there holds ∀ t ≥ 0, (S B A) (* n) (t) B(X ζ ,X) ≤ C a,n,ζ e at for a constant C a,n,ζ ∈ (0, ∞). dc.identifier.citationpages 4 dc.relation.ispartofseriestitle Cahier de recherche CEREMADE, Université Paris-Dauphine dc.identifier.urlsite https://hal.archives-ouvertes.fr/hal-01422273 dc.subject.ddclabel Analyse en dc.description.ssrncandidate non dc.description.halcandidate non dc.description.readership recherche dc.description.audience International dc.date.updated 2017-12-19T09:48:28Z hal.person.labIds 60
﻿

## Files in this item

FilesSizeFormatView

There are no files associated with this item.