Journal of the Institute of Mathematics of Jussieu

Research Article

Riesz bases of reproducing kernels in Fock-type spaces

Alexander Boricheva1 and Yurii Lyubarskiia2

a1 Centre de Mathématiques et Informatique, Université d'Aix-Marseille I, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France (borichev@cmi.univ-mrs.fr)

a2 Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway (yura@math.ntnu.no)

Abstract

In a scale of Fock spaces $\mathcal{F}_\varphi$ with radial weights xs03D5 we study the existence of Riesz bases of (normalized) reproducing kernels. We prove that these spaces possess such bases if and only if xs03D5(x) grows at most like (log x)2.

(Received December 05 2008)

(Accepted January 26 2009)

Keywords

  • Fock spaces;
  • Riesz bases;
  • reproducing kernels

AMS 2000 Mathematics subject classification

  • Primary 30H05;
  • Secondary 41A99