The rate of convergence of truncated hypersingular integrals generated by the Poisson and metaharmonic semigroups

ALİYEV İ., Cobanoglu S.

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, cilt.25, sa.12, ss.943-954, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 12
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1080/10652469.2014.940581
  • Dergi Adı: INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.943-954
  • Anahtar Kelimeler: metaharmonic semigroup, Bessel potentials, truncated hypersingular integrals, Riesz potentials, rate of convergence, Poisson semigroup, 44A35, 41A35, 26A33
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In harmonic analysis, an important problem is to obtain inversion formulas for the potential-type integral operators. The studies on this subject have been developed by the use of hypersingular integral technique. In this paper the families of truncated hypersingular integrals generated by the Poisson and metaharmonic semigroups and dependent on a parameter epsilon, are introduced. Then the connection between the order of smoothness of a given L-p-function phi and the rate of convergence of these families of truncated hypersingular integrals, which converge to phi when epsilon tends to 0, is obtained.