IDEAS home Printed from https://ideas.repec.org/a/bla/mathna/v295y2022i6p1113-1162.html
   My bibliography  Save this article

Generalized boundary triples, II. Some applications of generalized boundary triples and form domain invariant Nevanlinna functions

Author

Listed:
  • Volodymyr Derkach
  • Seppo Hassi
  • Mark Malamud

Abstract

The paper is a continuation of Part I and contains several further results on generalized boundary triples, the corresponding Weyl functions, and applications of this technique to ordinary and partial differential operators. We establish a connection between Post's theory of boundary pairs of closed nonnegative forms on the one hand and the theory of generalized boundary triples of nonnegative symmetric operators on the other hand. Applications to the Laplacian operator on bounded domains with smooth, Lipschitz, and even rough boundary, as well as to mixed boundary value problem for the Laplacian are given. Other applications concern with the momentum, Schrödinger, and Dirac operators with local point interactions. These operators demonstrate natural occurrence of ES$ES$‐generalized boundary triples with domain invariant Weyl functions and essentially selfadjoint reference operators A0.

Suggested Citation

  • Volodymyr Derkach & Seppo Hassi & Mark Malamud, 2022. "Generalized boundary triples, II. Some applications of generalized boundary triples and form domain invariant Nevanlinna functions," Mathematische Nachrichten, Wiley Blackwell, vol. 295(6), pages 1113-1162, June.
    • Handle: RePEc:bla:mathna:v:295:y:2022:i:6:p:1113-1162
    DOI: 10.1002/mana.202000049
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/mana.202000049
    Download Restriction: no
    File URL: https://libkey.io/10.1002/mana.202000049?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
    ---><---

    References listed on IDEAS

    as
    1. Olaf Post, 2016. "Boundary pairs associated with quadratic forms," Mathematische Nachrichten, Wiley Blackwell, vol. 289(8-9), pages 1052-1099, June.
    2. Volodymyr Derkach & Seppo Hassi & Mark Malamud, 2020. "Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions," Mathematische Nachrichten, Wiley Blackwell, vol. 293(7), pages 1278-1327, July.
    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. Volodymyr Derkach & Seppo Hassi & Mark Malamud, 2020. "Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions," Mathematische Nachrichten, Wiley Blackwell, vol. 293(7), pages 1278-1327, July.
    2. Olaf Post & Jan Simmer, 2021. "Graph‐like spaces approximated by discrete graphs and applications," Mathematische Nachrichten, Wiley Blackwell, vol. 294(11), pages 2237-2278, November.

    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:295:y:2022:i:6:p:1113-1162. 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: 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.