An integral transform associated to the Poisson integral and inversion of Flett potentials

Aliev I. A., Sezer S., Eryigit M.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, cilt.321, sa.2, ss.691-704, 2006 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 321 Sayı: 2
  • Basım Tarihi: 2006
  • Doi Numarası: 10.1016/j.jmaa.2005.08.086
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.691-704
  • Anahtar Kelimeler: Poisson integral, fractional integral, wavelet transform, inversion formulae, Flett potentials, WAVELET TRANSFORMS, BESSEL POTENTIALS, SPACES
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We introduce a new weighted wavelet-like transform, generated by the Poisson integral and a "wavelet measure." By making use of the relevant Calderon-type reproducing formula. we obtain an explicit inversion formula for the Flett potentials which are interpreted as negative fractional powers of the operator (E + Lambda). where Lambda = (-Delta)(1/2), Delta is the Laplacian and E is the identity operator. (c) 2005 Elsevier Inc. All rights reserved.