Mathematical Sciences

Lund University

  • Title: Berezin transforms of Fourier multipliers as shift operator expansions for Hilbert spaces of analytic functions in the unit disc
  • Description: In this paper we study Fourier multiplers on radially weighted Bergman Hilbert spaces of analytic functions in the unit disc. We relate the Berezin transform of such a Fourier multipler to a certain expansion formula in terms of the associated shift operator. We also show that the possibility of a specific operator formula of this type considered recently by Louhichi, Olofsson and Wennman implies non-vanishing of the associated reproducing kernel function.
  • Start Date: Feb. 13, 2012
  • Finished Date: Feb. 13, 2012
  • Supervisor: Anders Olofsson
  • Student: Andreas Andersson, (-)