Regularity of Non-Stationary Multivariate Subdivision
Provides a theoretical framework for analyzing non-stationary subdivision schemes, which is important for wavelet theory and approximation theory, but the results are incremental as they extend existing methods.
The paper develops a general approach for checking convergence and determining Hölder regularity of scalar multivariate non-stationary subdivision schemes with integer dilation matrices, and uses it to prove a conjecture on the Hölder regularity of generalized Daubechies wavelets.
In this paper, we study scalar multivariate non-stationary subdivision schemes with integer dilation matrix M=mI, m >=2, and present a general approach for checking their convergence and for determining their Hölder regularity. The combination of the concepts of asymptotic similarity and approximate sum rules allows us to link stationary and non-stationary settings and to employ recent advances in methods for exact computation of the joint spectral radius. As an application, we prove a recent conjecture on the Hölder regularity of the generalized Daubechies wavelets. We illustrate our results with several examples.