We study the construction of exponential frames and Riesz sequences for a class of fractal measures on ℝ^d generated by infinite convolution of discrete measures using the idea of frame towers and Riesz-sequence towers. The exactness and overcompleteness of the constructed exponential frame or Riesz sequence is completely classified in terms of the cardinality at each level of the tower. Using a version of the solution of the Kadison-Singer problem, known as the R_ϵ-conjecture, we show that all these measures contain exponential Riesz sequences of infinite cardinality. Furthermore, when the measure is the middle-third Cantor measure, or more generally for self-similar measures with no-overlap condition, there are always exponential Riesz sequences of maximal possible Beurling dimension.

我们研究指数框架和Riesz序列的结构的一类上ℝ分形措施^d通过使用帧塔和中Riesz序列塔的想法离散措施无限卷积生成。所构造的指数框架或Riesz序列的准确性和超完整性完全根据塔的每个级别的基数进行分类。使用Kadison-Singer问题的解决方案版本，称为R _ϵ-猜想，我们证明所有这些度量都包含无限基数的指数Riesz序列。此外，当测度是中三阶Cantor测度时，或更普遍地，对于无重叠条件的自相似测度，总是存在最大可能的Beurling维数的指数Riesz序列。