WILSON SYSTEM FOR TRIPLE REDUNDANCY

摘要

A Wilson orthonormal basis was constructed in 1991 by Daubechies, Jaffard and Journe from Gabor tight frame elements, when the redundancy of the Gabor system is 2. In 1994, Auscher gave a characterization of the atoms for which the Wilson system is an orthonormal basis. Afterwards, Grochenig posed a question whether the construction of an orthonormal Wilson basis is possible for a Gabor tight frame of redundancy 3. We give a partial positive answer to this question constructing in this case a Wilson system being a tight frame with bound 1.