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.