Continuous wavelet transform and uncertainty principle related to the Weinstein operator. Issue 4 (3rd April 2018)

• Record Type: Journal Article
• Authors: Hleili, K.
• Is Part Of: Integral transforms and special functions. Volume 29:Issue 4(2018)
• Page Start: 252
• Page End: 268
• Publication Date: 2018-04-03
• Subjects: Weinstein operator -- admissible wavelet -- wavelet transform -- uncertainty principles; 42B10 -- 42C40 -- 43A32; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2018.1428581
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: In this paper, we define and study the continuous wavelet transformT ψ associated with the Weinstein operator. Next, we analyse the concentration of this transform on sets of finite measure. We also establish an analogue of Heisenberg's inequality for wavelet transform. Last, we prove a quantitative version of Shapiro's mean dispersion theorem for the continuous wavelet transform.