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

2014/10/25 by Netanel Friedenberg, Friedenberg, Netanel, Peter M. Luthy +3
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1410.6876

openalex publication_date 2014/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 R² this criterion gives a complete characterization of such matrix groups.

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