l∞l∞-Stability for linear multiresolution algorithms: A new explicit approach. Part III: The 2-D case ★

This paper is devoted to the stability in the infinity norm for the Mallat’s multiresolution transform in 2-D. Explicit error bounds are presented by using some appropriate reformulations of the successive convolutions, some contraction properties and some alternative normalizations. The two new things in our study is the use of only basic rules and the derivation of explicit bounds. In particular, it can be understood for a wide part of the scientific community. Moreover, the results should be useful in mathematical, medical, physical, biological and engineering applications.