IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-981-13-6500-3_3.html
   My bibliography  Save this book chapter

Clifford Analysis, Dirac Operator and the Fourier Transform

In: Singular Integrals and Fourier Theory on Lipschitz Boundaries

Author

Listed:
  • Tao Qian

    (Macau University of Science and Technology, Macau Institute of Systems Engineering)

  • Pengtao Li

    (Qingdao University, School of Mathematics and Statistics)

Abstract

In this chapter, we state basic knowledge, notations and terminologies in Clifford analysis and some related results. These preliminaries will be used to establish the theory of convolution singular integrals and Fourier multipliers on Lipschitz surfaces. In Sect. 3.1, we give a brief survey on basics of Clifford analysis. In Sect. 3.2, we state the monogenic functions on sectors introduced by Li, McIntosh, Qian [1]. Section 3.3 is devoted to the Fourier transform theory on sectors established by [1]. Section 3.4 is based on the Möbius covarian of iterated Dirac operators by Peeter and Qian in [2]. In Sect. 3.5, we give a generalization of the Fueter theorem in the setting of Clifford algebras [3]. In Chaps. 6 and 7 , this generalization will be used to estimate the kernels of holomorphic Fourier multiplier operators on closed Lipschitz surfaces.

Suggested Citation

  • Tao Qian & Pengtao Li, 2019. "Clifford Analysis, Dirac Operator and the Fourier Transform," Springer Books, in: Singular Integrals and Fourier Theory on Lipschitz Boundaries, chapter 0, pages 67-115, Springer.
    • Handle: RePEc:spr:sprchp:978-981-13-6500-3_3
    DOI: 10.1007/978-981-13-6500-3_3
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Statistics

    Access and download statistics

    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:spr:sprchp:978-981-13-6500-3_3. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.