arXiv subjects

H. -Q. Bui

Publications and source records attributed to H. -Q. Bui.

3 recordsLinked to original sources

arXiv2012

Wavelet frame bijectivity on Lebesgue and Hardy spaces

We prove a sufficient condition for frame-type wavelet series in $L^p$, the Hardy space $H^1$, and BMO. For example, functions in these spaces are shown to have expansions in terms of the Mexican hat wavelet, thus giving a strong answer to an old question of Meyer. Bijectivity of the wavelet frame operator acting on Hardy space is established with the help of new frequency-domain estimates on the Calderón-Zygmund constants of the frame kernel.

math.CA↗

arXiv2011

Uniqueness for the continuous wavelet transform

Injectivity of the continuous wavelet transform acting on a square integrable signal is proved under weak conditions on the Fourier transform of the wavelet, namely that it is nonzero somewhere in almost every direction. For a bounded signal (not necessarily square integrable), we show that if the continuous wavelet transform vanishes identically, then the signal must be constant.

math.CA↗

arXiv2010

A note on the solution of the Mexican hat problem

We prove a technical estimate needed in our recent solution of the completeness question for the non-orthogonal Mexican hat wavelet system, in $L^p$ for $1<p<2$ and in the Hardy space $H^p$ for $2/3 < p \leq 1$.

math.CA↗