The cardinality of certain μM,D-orthogonal exponentials

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:362

Article

Li, Jian-Lin

关键词: Iterated function system;    Self-affine measure;    Orthogonal exponentials;    Non-spectral measure;   

DOI  :  10.1016/j.jmaa.2009.08.051

来源: Elsevier

【 摘 要 】

The self-affine measures mu(M,D) corresponding to the case (i) M = Pl(3), D = {0, e(1), e(2), e(3)} in the space R-3 and the case (ii) M = Pl(2), D = {0, e(1), e(2), e(1) + e(2)} in the plane R-2 are non-spectral, where p > 1 is odd, l(n) is the n x n identity matrix, and e(1),...,e(n) are the standard basis of unit column vectors in R-n. One of the non-spectral problem on mu(M,D) is to estimate the number of orthogonal exponentials in L-2(mu(M,D)) and to find them. In the present paper we show that, in both cases (i) and (ii), there are at most 4 mutually orthogonal exponentials in L-2(mu(M,D)) each. and the number 4 is the best. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

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