IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-0348-0667-1_20.html
   My bibliography  Save this book chapter

Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case

In: Operator Theory

Author

Listed:
  • Daniel Alpay

    (Ben-Gurion University of the Negev, Earl Katz Chair in Algebraic System Theory, Department of Mathematics)

  • Fabrizio Colombo

    (Politecnico di Milano, Dipartimento di Matematica)

  • Irene Sabadini

    (Politecnico di Milano, Dipartimento di Matematica)

Abstract

This chapter is a survey on recent developments in quaternionic Schur analysis. The first part is based on functions which are slice hyperholomorphic in the unit ball of the quaternions, and have modulus bounded by 1. These functions, which by analogy to the complex case are called Schur multipliers, are shown to be (as in the complex case) the source of a wide range of problems of general interest. They also suggest new problems in quaternionic operator theory, especially in the setting of indefinite inner product spaces. This chapter gives an overview on rational functions and their realizations, on the Hardy space of the unit ball, on the half-space of quaternions with positive real part, and on Schur multipliers, also discussing related results. For the purpose of comparison this chapter presents also another approach to Schur analysis in the quaternionic setting, in the framework of Fueter series. To ease the presentation most of the chapter is written for the scalar case, but the reader should be aware that the appropriate setting is often that of vector-valued functions.

Suggested Citation

  • Daniel Alpay & Fabrizio Colombo & Irene Sabadini, 2015. "Schur Analysis in the Quaternionic Setting: The Fueter Regular and the Slice Regular Case," Springer Books, in: Daniel Alpay (ed.), Operator Theory, edition 127, chapter 62, pages 1745-1786, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-0667-1_20
    DOI: 10.1007/978-3-0348-0667-1_20
    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

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:978-3-0348-0667-1_20. 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.