Perturbing semigroups by solving Stieltjes renewal equations

Odo Diekmann, Mats Gyllenberg, Horst Thieme, Glenn Webb

Research output: Contribution to journalArticle

20 Citations (Scopus)

Abstract

We develop a perturbation theory for strongly continuous semigroups and dual semigroups not based on perturbation of infinitesimal generators but on certain families of bounded linear operators describing the cumulative effect of the feedback. The theory extends the theory of perturbation of generators by bounded or relatively bounded linear operators. The theory is applied to problems of structured population dynamics which cannot, to the best of our knowledge, be treated using a more conventional perturbation theory.

Original languageEnglish (US)
Pages (from-to)155-181
Number of pages27
JournalDifferential and Integral Equations
Volume6
Issue number1
StatePublished - 1993

Fingerprint

Renewal Equation
Population dynamics
Semigroup
Bounded Linear Operator
Feedback
Perturbation Theory
Perturbation
Strongly Continuous Semigroups
Structured Populations
Infinitesimal Generator
Population Dynamics
Generator

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Perturbing semigroups by solving Stieltjes renewal equations. / Diekmann, Odo; Gyllenberg, Mats; Thieme, Horst; Webb, Glenn.

In: Differential and Integral Equations, Vol. 6, No. 1, 1993, p. 155-181.

Research output: Contribution to journalArticle

Diekmann, O, Gyllenberg, M, Thieme, H & Webb, G 1993, 'Perturbing semigroups by solving Stieltjes renewal equations', Differential and Integral Equations, vol. 6, no. 1, pp. 155-181.
Diekmann, Odo ; Gyllenberg, Mats ; Thieme, Horst ; Webb, Glenn. / Perturbing semigroups by solving Stieltjes renewal equations. In: Differential and Integral Equations. 1993 ; Vol. 6, No. 1. pp. 155-181.
@article{787a772e965d43b98b64ec6639769240,
title = "Perturbing semigroups by solving Stieltjes renewal equations",
abstract = "We develop a perturbation theory for strongly continuous semigroups and dual semigroups not based on perturbation of infinitesimal generators but on certain families of bounded linear operators describing the cumulative effect of the feedback. The theory extends the theory of perturbation of generators by bounded or relatively bounded linear operators. The theory is applied to problems of structured population dynamics which cannot, to the best of our knowledge, be treated using a more conventional perturbation theory.",
author = "Odo Diekmann and Mats Gyllenberg and Horst Thieme and Glenn Webb",
year = "1993",
language = "English (US)",
volume = "6",
pages = "155--181",
journal = "Differential and Integral Equations",
issn = "0893-4983",
publisher = "Khayyam Publishing, Inc.",
number = "1",

}

TY - JOUR

T1 - Perturbing semigroups by solving Stieltjes renewal equations

AU - Diekmann, Odo

AU - Gyllenberg, Mats

AU - Thieme, Horst

AU - Webb, Glenn

PY - 1993

Y1 - 1993

N2 - We develop a perturbation theory for strongly continuous semigroups and dual semigroups not based on perturbation of infinitesimal generators but on certain families of bounded linear operators describing the cumulative effect of the feedback. The theory extends the theory of perturbation of generators by bounded or relatively bounded linear operators. The theory is applied to problems of structured population dynamics which cannot, to the best of our knowledge, be treated using a more conventional perturbation theory.

AB - We develop a perturbation theory for strongly continuous semigroups and dual semigroups not based on perturbation of infinitesimal generators but on certain families of bounded linear operators describing the cumulative effect of the feedback. The theory extends the theory of perturbation of generators by bounded or relatively bounded linear operators. The theory is applied to problems of structured population dynamics which cannot, to the best of our knowledge, be treated using a more conventional perturbation theory.

UR - http://www.scopus.com/inward/record.url?scp=84972525241&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84972525241&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84972525241

VL - 6

SP - 155

EP - 181

JO - Differential and Integral Equations

JF - Differential and Integral Equations

SN - 0893-4983

IS - 1

ER -