Representation theorems for the Mexican hat wavelet transform. (7th February 2020)

• Record Type: Journal Article
• Authors: Singh, Abhishek; Raghuthaman, Nikhila; Rawat, Aparna; Singh, Jagdev
• Is Part Of: Mathematical methods in the applied sciences. Volume 43:Number 7(2020)
• Page Start: 3914
• Page End: 3924
• Publication Date: 2020-02-07
• Subjects: Mexican hat wavelet transform -- wavelet transform -- weierstrass transform; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.6158
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we discuss representation theorems for Mexican hat wavelet transform with determining function α 2 ( y ) belonging to different class of functions. The classes H, A [ p, q ], B [ p, q ], and C [ p, q ] are characterized by the Mexican hat wavelet transform. Also, we investigate the convergence of the transform with its boundedness property. Furthermore, some representation theorems for locally bounded variation and locally Lebesgue integrable function are established.