Advances in Pure Mathematics

Volume 11, Issue 8 (August 2021)

ISSN Print: 2160-0368   ISSN Online: 2160-0384

Google-based Impact Factor: 0.48  Citations  

Non-Spectral Problem of Self-Affine Measures in R3

HTML  XML Download Download as PDF (Size: 340KB)  PP. 717-734  
DOI: 10.4236/apm.2021.118047    224 Downloads   754 Views  
Author(s)

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 in L2(μM,D), where the number 4 is the best possible. This extends several known conclusions.

Share and Cite:

Yuan, Y. (2021) Non-Spectral Problem of Self-Affine Measures in R3. Advances in Pure Mathematics, 11, 717-734. doi: 10.4236/apm.2021.118047.

Cited by

No relevant information.

Copyright © 2025 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.