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Locally bounded linear differential operators

  1. Aug 29, 2013 #1
    The following is a problem statement.

    locally bounded (or locally (weakly) compact) differential operators of the Schwartz space of smooth functions on a sigma-compact manifold

    I realize this is very abstract. I expect the solution to be just as abstract.

    Thanks in advance.
    Last edited: Aug 29, 2013
  2. jcsd
  3. Aug 29, 2013 #2
    That's not a question, and we're not in the habit of doing people's work for them anyway. What is the problem you're working on, and what have you done so far?
  4. Aug 29, 2013 #3
    I believe the above problem is the core of the Navier-Stokes equation. It describes the inner working of the NS equations from a mathematical operator's point-of-view.

    I have studied bornology from Hogbe-Nlend's books Bornology and Functional Analysis; Nuclear and Conuclear Spaces. According to Wikipedia, bornology is the minimum amount of structure to address boundedness of sets and functions.

    The next closest thing I have come across is Nuclear Convex Bornological Spaces.
    Last edited: Aug 29, 2013
  5. Aug 29, 2013 #4
    What problem? You just said a kind of operator. It would be like me starting a thread and saying "bounded linear function". What are you trying to prove?
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