Local Convergence of the Continuous and Semi-Discrete Wavelet Transform in Lp(R)

Abstract

The smoothness of functions f in the space $L^p\left(\mathbb{R}\right)$ with $1<p<\infty$ is studied through the local convergence of the continuous wavelet transform of f. Additionally, we study the smoothness of functions in $L^p\left(\mathbb{R}\right)$ by means of the local convergence of the semi-discrete wavelet transform.