IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v3y2015i3p615-625d52284.html
   My bibliography  Save this article

Reproducing Kernel Hilbert Space vs. Frame Estimates

Author

Listed:
  • Palle E. T. Jorgensen

    (Department of Mathematics, The University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA)

  • Myung-Sin Song

    (Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Box 1653, Edwardsville, IL 62026, USA)

Abstract

We consider conditions on a given system F of vectors in Hilbert space H , forming a frame, which turn H into a reproducing kernel Hilbert space. It is assumed that the vectors in F are functions on some set Ω . We then identify conditions on these functions which automatically give H the structure of a reproducing kernel Hilbert space of functions on Ω. We further give an explicit formula for the kernel, and for the corresponding isometric isomorphism. Applications are given to Hilbert spaces associated to families of Gaussian processes.

Suggested Citation

  • Palle E. T. Jorgensen & Myung-Sin Song, 2015. "Reproducing Kernel Hilbert Space vs. Frame Estimates," Mathematics, MDPI, vol. 3(3), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:3:p:615-625:d:52284
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/3/3/615/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/3/3/615/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Alvaro Nosedal-Sanchez & Curtis B. Storlie & Thomas C.M. Lee & Ronald Christensen, 2012. "Reproducing Kernel Hilbert Spaces for Penalized Regression: A Tutorial," The American Statistician, Taylor & Francis Journals, vol. 66(1), pages 50-60, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Tong, Xiaojun & He, Zhuoqiong Chong & Sun, Dongchu, 2018. "Estimating Chinese Treasury yield curves with Bayesian smoothing splines," Econometrics and Statistics, Elsevier, vol. 8(C), pages 94-124.

    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:gam:jmathe:v:3:y:2015:i:3:p:615-625:d:52284. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.