Twin semigroups and delay equations

Research output: Working paperPreprintAcademic

Abstract

In the standard theory of delay equations, the fundamental solution does not 'live' in the state space. To eliminate this age-old anomaly, we enlarge the state space. As a consequence, we lose the strong continuity of the solution operators and this, in turn, has as a consequence that the Riemann integral no longer suffices for giving meaning to the variation-of-constants formula. To compensate, we develop the Stieltjes-Pettis integral in the setting of a norming dual pair of spaces. Part I provides general theory, Part II deals with "retarded" equations, and in Part III we show how the Stieltjes integral enables incorporation of unbounded perturbations corresponding to neutral delay equations.
Original languageEnglish
PublisherarXiv
Pages1-75
DOIs
Publication statusPublished - 8 Jun 2019

Keywords

  • math.DS
  • math.CA
  • math.FA
  • 34F

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