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Volume 31, Issue 4
Spectral Self-Affine Measures on the Generalized Three Sierpinski Gasket

Y. B. Yuan

Anal. Theory Appl., 31 (2015), pp. 394-406.

Published online: 2017-10

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  • 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.

  • AMS Subject Headings

28A80, 42C05

  • Copyright

COPYRIGHT: © Global Science Press

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@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 = {

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.

}, 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} }
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 -

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.

Y. B. Yuan. (2017). Spectral Self-Affine Measures on the Generalized Three Sierpinski Gasket. Analysis in Theory and Applications. 31 (4). 394-406. doi:10.4208/ata.2015.v31.n4.5
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