Some Localization Properties of the Lp Continuous Wavelet Transform. (2nd January 2018)

• Record Type: Journal Article
• Authors: Medina, Juan Miguel; Cernuschi-Frías, Bruno
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 1(2018)
• Page Start: 87
• Page End: 99
• Publication Date: 2018-01-02
• Subjects: Continuous wavelet transform -- uncertainty principles -- Lp spaces; 42C40 -- 26D15 -- 42A99 -- 42C99; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1354887
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: We shall prove some simultaneous localization or concentration inequalities for the continuous wavelet transform. We will also show that simultaneous localization in the scale-time(space) is impossible, in the sense that the scale sections of the support of wavelet transform of a nonnull L p -function can not have finite Lebesgue measure. Finally, some properties of the support of continuous wavelet transform of band-limited functions are studied.