Parabolic-Like Wavelet Transforms and Relevant Reproducing Formulas
| Autor: | Ilham A. Aliev, Cagla Sekin |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Generalization Applied Mathematics General Mathematics 010102 general mathematics Gauss Wavelet transform 020206 networking & telecommunications 02 engineering and technology Function (mathematics) 01 natural sciences Measure (mathematics) symbols.namesake Wavelet Fourier analysis 0202 electrical engineering electronic engineering information engineering symbols 0101 mathematics Connection (algebraic framework) Analysis Mathematics |
| Zdroj: | Journal of Fourier Analysis and Applications. 27 |
| ISSN: | 1531-5851 1069-5869 |
| DOI: | 10.1007/s00041-021-09846-x |
| Popis: | 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 $$L_{p}(\mathbb {R}^{n+1})$$ -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. |
| Databáze: | OpenAIRE |
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