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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 294182, 9 pages
http://dx.doi.org/10.1155/2014/294182
Research Article

Nonspectrality of Certain Self-Affine Measures on

1College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
2Applied Mathematics Department, Yuncheng University, Yuncheng Shanxi 044000, China

Received 11 September 2013; Accepted 30 November 2013; Published 8 January 2014

Academic Editor: Natig M. Atakishiyev

Copyright © 2014 Gui-Bao Gao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We will determine the nonspectrality of self-affine measure corresponding to , , and in the space is supported on , where , and are the standard basis of unit column vectors in , and there exist at most mutually orthogonal exponential functions in , where the number is the best. This generalizes the known results on the spectrality of self-affine measures.