INFINITE ORTHOGONAL EXPONENTIALS OF A CLASS OF SELF-AFFINE MEASURES

Zhi-Min Wang, Xin-Han Dong () and Ye Wang
Additional contact information
Zhi-Min Wang: School of Science, Hunan University of Technology, Zhuzhou, Hunan 412007, P. R. China
Xin-Han Dong: ��Key Laboratory of High Performance Computing and Stochastic, Information Processing (Ministry of Education of China), College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
Ye Wang: ��College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 03, 1-9

Abstract: In this paper, we study infinite families of orthogonal exponentials of some self-affine measures. The digit set D = 0 0 , 1 0 , 0 2 and any 2 × 2 expanding integer matrix M ∈ M2(ℤ) can generate a self-affine measure μM,D. Let 𠜖7 = (1 3, 1 3)t and M∗ := 3M̃ + M α be the transposed conjugate of M, where M̃ ∈ M2(ℤ) and the elements of Mα come from {0, 1, 2}. In this paper, we prove the following results. For Mα ∈{Mα : Mα𠜖7 ∈ ℤ2,det(M α) ∈ 3ℤ}, μM,D is a spectral measure. For Mα ∈{Mα : Mα2𠜖 7 ∈ ℤ2,M α𠜖7∉ℤ2,det(M α) ∈ 3ℤ}, there are infinite families of orthogonal exponentials, but none of them forms an orthogonal basis in L2(μ M,D).

Keywords: Self-Affine Measure; Spectrum; Spectral Measure; Orthogonal Exponential Functions (search for similar items in EconPapers)
Date: 2021
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X21500547
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:29:y:2021:i:03:n:s0218348x21500547

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X21500547

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().