Wavelets

Guido Weiss: From Immigrant Boy to Internationally Renowned Mathematician

“…The most frequent among them is Guido's close and long-time friend and colleague Edward (Ed) Wilson. Their expository article in the Notices [35], jointly with Demetrio Labate, is an excellent survey of many developments in the subject up to 2013.…”

Convergence in L p ([0, T]) of Wavelet Expansions of φ-Sub-Gaussian Random Processes

“…This class plays an important role in generalizations of various theoretical properties of Gaussian processes. In addition to classical applications of ϕ-sub-Gaussian random processes in signal processing, the results can also be used in new areas, like compressed sensing and actuarial modelling, consult, for example, Labate et al 2013, Vershynin 2012, Yamnenko 2006 It would be of interest to adopt and specify the results for different wavelet bases, which satisfy the assumptions of the theorems, for example, Daubechies, Battle-Lemarie and Meyer wavelets; -to examine the tightness of the estimates by simulations.…”

Wavelet transform on the torus: A group theoretical approach

“…A way out could be to impose additional conditions to the support of ψ, like extending it to a ring around the origin (0, 0) [17], or to introduce extra group parameters like rotations, shears, etc. Also, in the discrete case, frames in R n , with n ≥ 2, with a single dilation are constructed from more than one (in fact at least 2 n − 1) admissible function [24,25].…”