Parabolic-Like Wavelet Transforms and Relevant Reproducing Formulas

Aliev I. A., SEKİN Ç.

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, cilt.27, sa.3, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 27 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00041-021-09846-x
  • Dergi Adı: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: Wavelet transforms, Wavelet measure, Inversion formulas, Parabolic potentials, Gauss kernel, Poisson kernel, INVERSION
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We introduce new anisotropic wavelet-type transforms generated by two components: a wavelet measure (or a wavelet function) and a kernel function that naturally generalizes the Gauss and Poisson kernels. The analogues of Calderon's reproducing formula are established in the framework of the L-p(Rn+1)-theory. These wavelet-type transforms have close connection with a significant generalization of the classical parabolic-Riesz and parabolic-Bessel potentials and can be used to find explicit inversion formulas for the generalized parabolic-type potentials.