Mexican hat wavelet transform of generalized functions in \(\mathcal{G}^{\prime}\) spaces

DOI10.1007/s12044-021-00627-6zbMath1482.42088OpenAlexW3206453989MaRDI QIDQ2052865

Abhishek Singh, Aparna Rawat

Publication date: 29 November 2021

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-021-00627-6

zbMATH Keywords

wavelet transformWeierstrass transformgeneralized functions.Mexican hat wavelet transform (MHWT)

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Operations with distributions and generalized functions (46F10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Cites Work

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• The wavelet transform
• The Weierstrass transform for a class of generalized functions
• A new theory for Fourier analysis. IV: Basic multiplication and convolution on the dual space
• A new theory for Fourier analysis. V: Generalized multiplication and convolution on the dual space
• Mexican hat wavelet transform of distributions
• Paley–Wiener–Schwartz type theorem for the wavelet transform
• A Miniature Theory in Illustration of the Convolution Transform

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