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https://doi.org/10.1007/BF02788699

has been cited by the following article:

• TITLE: Non-Spectral Problem of Self-Affine Measures in R3

  AUTHORS: Yanbo Yuan

  KEYWORDS: Iterated Function System (IFS), Self-Affine Measure, Orthogonal Exponentials

  JOURNAL NAME: Advances in Pure Mathematics, Vol.11 No.8, August 12, 2021

  ABSTRACT: The problems of determining the spectrality or non-spectrality of a measure have been received much attention in recent years. One of the non-spectral problems on μM,D is to estimate the number of orthogonal exponentials in L2(μM,D). In the present paper, we establish some relations inside the zero set by the Fourier transform of the self-affine measure μM,D. Based on these facts, we show that μM,D is a non-spectral measure and there exist at most 4 mutually orthogonal exponential functions inL2(μM,D), where the number 4 is the best possible. This extends several known conclusions.