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Parabolic-Like Wavelet Transforms and Relevant Reproducing Formulas

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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 \(L_{p}(\mathbb {R}^{n+1})\)-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.

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Acknowledgements

The authors are deeply grateful to the editor and anonymous referees for their valuable suggestions that greatly improved the article.

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Correspondence to Ilham A. Aliev.

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Communicated by Stephan Dahlke.

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Aliev, I.A., Sekin, C. Parabolic-Like Wavelet Transforms and Relevant Reproducing Formulas. J Fourier Anal Appl 27, 44 (2021). https://doi.org/10.1007/s00041-021-09846-x

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  • DOI: https://doi.org/10.1007/s00041-021-09846-x

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