IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v29y2021i03ns0218348x21500547.html
   My bibliography  Save this article

Infinite Orthogonal Exponentials Of A Class Of Self-Affine Measures

Author

Listed:
  • 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)

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).

Suggested Citation

  • Zhi-Min Wang & Xin-Han Dong & Ye Wang, 2021. "Infinite Orthogonal Exponentials Of A Class Of Self-Affine Measures," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-9, May.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:03:n:s0218348x21500547
    DOI: 10.1142/S0218348X21500547
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X21500547
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0218348X21500547?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:fracta:v:29:y:2021:i:03:n:s0218348x21500547. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.