Stability of Multiscale Transformations.
Wolfgang Dahmen · 1995
After briefly reviewing the interrelation between Riesz-bases, biorthogonality and a certain stability notion for multiscale basis transformations we establish a basic stability criterion for the underlying multiresolutions spaces. The main tools are taken from the theory of interpolation of Banach spaces. Furthermore, we highlight a few consequences pertaining to norm equivalences of Besov/Sobolev-type. (orig.)