Parabolic-Like Wavelet Transforms and Relevant Reproducing Formulas
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, vol.27, no.3, 2021 (SCI-Expanded)
- Publication Type: Article / Article
- Volume: 27 Issue: 3
- Publication Date: 2021
- Doi Number: 10.1007/s00041-021-09846-x
- Journal Name: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
- Keywords: Wavelet transforms, Wavelet measure, Inversion formulas, Parabolic potentials, Gauss kernel, Poisson kernel, INVERSION
- Akdeniz University Affiliated: Yes
Abstract
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.