Wavelet-type transform and bessel potentials associated with the generalized translation

Aliev I., Eryigit M.

INTEGRAL EQUATIONS AND OPERATOR THEORY, vol.51, no.3, pp.303-317, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 3
  • Publication Date: 2005
  • Doi Number: 10.1007/s00020-004-1333-5
  • Journal Name: INTEGRAL EQUATIONS AND OPERATOR THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.303-317
  • Keywords: wavelet-type transform, Calderon's reproducing formula, Bessel potentials, generalized translation operator, PARABOLIC POTENTIALS
  • Akdeniz University Affiliated: Yes

Abstract

Wavelet-type transform associated with singular Laplace-Bessel differential operator Delta(v) = Sigma(k=1)(n) partial derivative(2)/partial derivative x(k)(2) + 2v/x(n) (.) partial derivative/partial derivative x(n) is introduced and the relevant Calderon-type reproducing formula is established. Representations of the generalized Bessel potentials (E - Delta(v))(-alpha/2) f, (Rea > 0) and their inverses via the wavelet-type transform are obtained.