C0 -semigroups of 2-isometries and Dirichlet spaces

  1. Eva A. Gallardo-Gutiérrez 1
  2. Jonathan R. Partington 2
  1. 1 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

  2. 2 University of Leeds
    info

    University of Leeds

    Leeds, Reino Unido

    ROR https://ror.org/024mrxd33

Journal:
Revista matemática iberoamericana

ISSN: 0213-2230

Year of publication: 2018

Volume: 34

Issue: 3

Pages: 1415-1425

Type: Article

DOI: 10.4171/RMI/1030 DIALNET GOOGLE SCHOLAR

More publications in: Revista matemática iberoamericana

Abstract

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.

Data source: Dialnet