一类自相似tile成为框架集的充分必要条件

摘要

本文研究了数字集具有严格乘积形式的自相似tile成为框架集的问题.利用Zak变换,证明了自相似tile是框架集的充要条件是其数字集D={0,1,2…,N-1}.%In this article, the authors study the condition that a self-similar tile with a strictly product form digit set D is a frame set. By Zak transform, they get that the tile is a frame set iff the digit set D = {0,1,2, · · · , N - 1}.