A family of Mexican hat wavelet transforms associated with an isometry in the heat equation. (13th May 2021)

• Record Type: Journal Article
• Authors: Srivastava, Hari M.; Singh, Abhishek; Rawat, Aparna; Singh, Shubha
• Is Part Of: Mathematical methods in the applied sciences. Volume 44:Number 14(2021)
• Page Start: 11340
• Page End: 11349
• Publication Date: 2021-05-13
• Subjects: Green's function -- heat equation -- Hilbert spaces with reproducing kernels -- Mexican hat wavelets -- Wavelet transforms -- Weierstrass transform; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.7492
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.