Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Function Spaces C^k

  1. Apr 11, 2013 #1
    Could you check my understanding of these facts please:

    First is there a difference between the notations "function space" and "Differentiation Class" ? Methinks they are one.

    Second, a function ##f## is said to be in ##C^k \iff \ f^{(k)}## exists and is in ##C^0##.

    Third, if a function has discontinuities then it belong to ##C^{-1}##

    Thank you
     
  2. jcsd
  3. Apr 11, 2013 #2

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    A function space is something more general. The spaces ##C^k##are certainly function spaces, but there are many more.

    Yes.

    I have encountered ##C^{-1}## before, but I forgot what it was. I kind of doubt that it is standard terminology anyway. Do you have a reference for this?
     
  4. Apr 11, 2013 #3
    Unfortunately I can only quote the "Wikipedia" page on "Smooth Functions". I tried to do a google search for the term to no avail.
     
  5. Apr 11, 2013 #4

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    The way I've seen it defined is that ##C^{-1}## has functions that are piecewise continuous. So they have discontinuities, but only a limited number. But I don't have a reference either. It's not very important anyway.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook