C0 -semigroups of 2-isometries and Dirichlet spaces

• Eva A. Gallardo-Gutiérrez ^[1] ; Jonathan R. Partington ^[2]
  1. [1] Universidad Complutense de Madrid

     Universidad Complutense de Madrid

     Madrid, España

     
  2. [2] University of Leeds

     University of Leeds

     Reino Unido

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 34, Nº 3, 2018, págs. 1415-1425
• Idioma: inglés
• DOI: 10.4171/RMI/1030
• Texto completo no disponible (Saber más ...)
• Resumen

  • In the context of a theorem of Richter, we establish a similarity between C0-semigroups of analytic 2-isometries {T(t)}t≥0 acting on a Hilbert space H and the multiplication operator semigroup {Mϕt}t≥0 induced by ϕt(s)=exp(−st) for s in the right-half plane C+ acting boundedly on weighted Dirichlet spaces on C+. As a consequence, we derive a connection with the right shift semigroup {St}t≥0 given by Stf(x)={0f(x−t) if 0≤x≤t, if x>t, acting on a weighted Lebesgue space on the half line R+ and address some applications regarding the study of the invariant subspaces\linebreak of C0-semigroups of analytic 2-isometries.