IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v297y2024i7p2488-2516.html
   My bibliography  Save this article

On the structure of Nevanlinna measures

Author

Listed:
  • Mitja Nedic
  • Eero Saksman

Abstract

In this paper, we study the structural properties of Nevanlinna measures, that is, Borel measures that arise in the integral representation of Herglotz–Nevanlinna functions. In particular, we give a characterization of these measures in terms of their Fourier transform, characterize measures supported on hyperplanes including extremal measures, describe the structure of the singular part of the measures when some variable are set to a fixed value, and provide estimates for the measure of expanding and shrinking cubes. Corresponding results are stated also in the setting of the polydisc where applicable, and some of our proofs are actually performed via the polydisc.

Suggested Citation

  • Mitja Nedic & Eero Saksman, 2024. "On the structure of Nevanlinna measures," Mathematische Nachrichten, Wiley Blackwell, vol. 297(7), pages 2488-2516, July.
    • Handle: RePEc:bla:mathna:v:297:y:2024:i:7:p:2488-2516
    DOI: 10.1002/mana.202200135
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202200135
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.202200135?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
    ---><---

    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:bla:mathna:v:297:y:2024:i:7:p:2488-2516. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0025-584X .

    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.