Fourier Bases And Fourier Frames On Self-Affine Measures

Abstract

This paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal set. This method helps us settle down a long-standing conjecture that Hadamard triples generate self-affine spectral measures. It also gives us non-trivial examples of fractal measures with Fourier frames. Furthermore, a new avenue is open to investigate whether the Middle-Third-Cantor measure admits Fourier frames.

Publication Date

1-1-2017

Publication Title

Trends in Mathematics

Volume

PartF3

Number of Pages

87-111

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/978-3-319-57805-7_5

Socpus ID

85028755108 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85028755108

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