English

Uniqueness for the continuous wavelet transform

Classical Analysis and ODEs 2011-03-18 v1

Abstract

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.

Keywords

Cite

@article{arxiv.1103.3317,
  title  = {Uniqueness for the continuous wavelet transform},
  author = {H. -Q. Bui and R. S. Laugesen},
  journal= {arXiv preprint arXiv:1103.3317},
  year   = {2011}
}

Comments

7 pages

R2 v1 2026-06-21T17:40:38.726Z