English

An Elementary Eigenvalue Criterion for One-Parameter Dilation Groups to Admit a Continuous Wavelet

Classical Analysis and ODEs 2014-10-28 v1

Abstract

In this article, we present a simple criterion for checking whether a one-parameter matrix group of dilations admits a continuous wavelet. This criterion involves only checking that the eigenvalues of the symmetric part of the matrix have the same sign. In R2R^2 this criterion gives a complete characterization of such matrix groups.

Keywords

Cite

@article{arxiv.1410.6876,
  title  = {An Elementary Eigenvalue Criterion for One-Parameter Dilation Groups to Admit a Continuous Wavelet},
  author = {Netanel Friedenberg and Peter M. Luthy and Guido L. Weiss},
  journal= {arXiv preprint arXiv:1410.6876},
  year   = {2014}
}

Comments

11 pages

R2 v1 2026-06-22T06:36:12.839Z