Reproducing kernels for harmonic Besov spaces on the ball

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Gergun S., KAPTANOĞLU H. T., ÜREYEN A. E.

COMPTES RENDUS MATHEMATIQUE, vol.347, no.13-14, pp.735-738, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 347 Issue: 13-14
  • Publication Date: 2009
  • Doi Number: 10.1016/j.crma.2009.04.016
  • Journal Name: COMPTES RENDUS MATHEMATIQUE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.735-738
  • Anadolu University Affiliated: No

Abstract

Besov spaces of harmonic functions on the unit ball of R '' are defined by requiring Sufficiently high-order derivatives of functions lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels turn out to be weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. To cite this article: S. Gergun et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.