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A family of Mexican hat wavelet transforms associated with an isometry in the heat equation
Author(s) -
Srivastava Hari M.,
Singh Abhishek,
Rawat Aparna,
Singh Shubha
Publication year - 2021
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.7492
Subject(s) - mathematics , heat equation , isometry (riemannian geometry) , wavelet , mathematical analysis , pure mathematics , wavelet transform , artificial intelligence , computer science
In this paper, Green's function of the heat equation is used to obtain one of the forms in a family of Mexican hat wavelet transforms. By implementing the theory of reproducing kernels, an isometry in the heat equation is also investigated. Further, a natural inversion is established for the Mexican hat wavelet transform. Several related recent investigations are also considered.