Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 4 : pp. 394–406
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n4.5
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 4 : pp. 394–406
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
Keywords: Compatible pair orthogonal exponentials spectral measure.