TY - JOUR
T1 - Spectral Self-Affine Measures on the Generalized Three Sierpinski Gasket
AU - Y. B. Yuan
JO - Analysis in Theory and Applications
VL - 4
SP - 394
EP - 406
PY - 2017
DA - 2017/10
SN - 31
DO - http://doi.org/10.4208/ata.2015.v31.n4.5
UR - https://global-sci.org/intro/article_detail/ata/4647.html
KW - Compatible pair, orthogonal exponentials, spectral measure.
AB - <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>