Mexican hat wavelet transform of distributions. Issue 6 (2nd June 2016)

• Record Type: Journal Article
• Authors: Pathak, R. S.; Singh, Abhishek
• Is Part Of: Integral transforms and special functions. Volume 27:Issue 6(2016)
• Page Start: 468
• Page End: 483
• Publication Date: 2016-06-02
• Subjects: Distribution space -- wavelet transform -- Mexican hat wavelet -- Weierstrass transform; 44A15 -- 42C15 -- 46F12; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2016.1155569
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: Theory of Weierstrass transform is exploited to derive many interesting new properties of the Mexican hat wavelet transform. A real inversion formula in the differential operator form for the Mexican hat wavelet transform is established. Mexican hat wavelet transform of distributions is defined and its properties are studied. An approximation property of the distributional wavelet transform is investigated which is supported by a nice example.