@Article{ATA-31-394,
author = {Y. B. Yuan},
title = {Spectral Self-Affine Measures on the Generalized Three Sierpinski Gasket},
journal = {Analysis in Theory and Applications},
year = {2017},
volume = {31},
number = {4},
pages = {394--406},
abstract = {<p style="text-align: justify;">The self-affine measure $\mu_{M,D}$ associated with an iterated function system$\{\phi_{d} (x)=M^{-1}(x+d)\}_{d\in D}$ is uniquely determined. It only depends upon an expanding matrix $M$ and a finite digit set $D$. In the present paper we give some sufficient conditions for finite and infinite families of orthogonal exponentials. Such research is necessary to further understand the non-spectral and spectral of $\mu_{M,D}$. As an application, we show that the $L^2(\mu_{M, D})$ space has infinite families of orthogonal exponentials on the generalized three Sierpinski gasket. We then consider the spectra of a class of self-affine measures which extends several known conclusions in a simple manner.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2015.v31.n4.5},
url = {http://global-sci.org/intro/article_detail/ata/4647.html}
}