Convergence and smoothness of tensor-product of two non-uniform linear subdivision schemes.

Abstract The aim of this short note is to provide a rigorous proof that the tensor product of two non-uniform linear convergent subdivision schemes converges and has the same regularity as the minimal regularity of the univariate schemes. It extends results that are known for the uniform linear case and are based on symbols, a notion which is no longer available in the non-uniform setting. [ABSTRACT FROM AUTHOR]