Quantitative Uncertainty Principles Associated with the Sturm-Liouville Wavelet Transform

Abstract

The Sturm-Liouville wavelet transform (SLWT) is a novel addition to the class of Sturm-Liouville transforms, which has gained a respectable status in the realm of time-frequency signal analysis within a short span of time. Given that the study of time-frequency analysis is of both theoretically interesting and practically useful, the aim of this paper is to explore a class of quantitative uncertainty principles (UP) associated with SLWT, including Faris local-type UP, Shannon-type UP, Donoho-Stark-type UP and Benedicks-type UP.