Non-spectral self-affine measure problem on the plane domain

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:369

Article

Yuan, Yan-Bo^1,2 

[1] NW Normal Univ, Coll Math & Informat Sci, Lanzhou 730070, Peoples R China

[2] Shaanxi Normal Univ, Coll Math & Informat Sci, Xian, Peoples R China

关键词: Iterated function system (IFS);    Self-affine measure;    Orthogonal exponentials;   

DOI  :  10.1016/j.jmaa.2010.03.030

来源: Elsevier

【 摘 要 】

The self-affine measure mu(M,D) corresponding to an expanding integer matrix [GRAPHICS] is supported on the attractor (or invariant set) of the iterated function system {phi(d)(x) = m(-1)(x +d)}(d epsilon D). In the present paper we show that if (a + d)(2) = 4(ad - bc) and ad - bc is not a multiple of 3, then there exist at most 3 mutually orthogonal exponential functions in L-2(mu(M,D)), and the number 3 is the best. This extends several known results on the non-spectral self-affine measure problem. The proof of such result depends on the characterization of the zero set of the Fourier transform (mu) over cap (M,D), and provides a way of dealing with the non-spectral problem. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

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