arXiv subjects

Qi-Rong Deng

Publications and source records attributed to Qi-Rong Deng.

2 recordsLinked to original sources

arXiv2026

Spectrality of Moran-Type Measures Generated by Two-Element and Three-Element Digit Sets

The necessary and sufficient conditions for the Moran-type measures generated by two-element and three-element digit sets to be spectral have been given. The main result indicates that the spectrality of such a Moran-type measure is completely determined by the number of 2-factors and 3-factors in the zero set of the Fourier transform of each term in the convolution. The proof shows that, without the existence of Hadamard triples, the problem becomes much more complicated and difficult than the case with the existence of Hadamard triples.

math.CA↗

arXiv2026

Moran-Type Iterated Function Systems and Dimensions of Moran Self-Similar Sets

Moran-type iterated function systems (Moran-type IFS or MIFS) are defined by a sequence of iterated function systems, and their basic theoretical framework is established. We define Moran-type attractors and invariant probability measures associated with a sequence of probability weight vectors. Furthermore, separation conditions for MIFS are introduced, and the dimension theory of Moran-type self-similar sets is investigated. Appropriate examples are provided to illustrate and support the definitions and results.

math.DS↗