Results 1 to 2 of 2

Math Help - smooth function

  1. #1
    Junior Member
    Joined
    May 2008
    Posts
    50

    smooth function

    I have a problem finding a smooth function on R^k that equals 1 on the ball of radius a, zero outside of the ball of radius b, and is strictly between zero and 1 at intermediate points, where 0<a<b. Any suggestion?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    675
    Thanks
    32
    Let r=(a+b)/2 and g the function given by r^k exp(-1/(1-|x|^2/r)) if |x|<r and 0 elsewhere. We denote by h the characteristic function of the ball of center 0 and radius r. Put f(x) =\int_{\mathbb R^k}g(x-y)h(y)dy.

    Sorry, \LaTeX doesn't work.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: March 26th 2011, 09:10 AM
  2. Smooth Function R^3 -> R^4
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 12th 2011, 10:54 AM
  3. Replies: 1
    Last Post: October 7th 2010, 08:54 PM
  4. how to determine when a function is smooth
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 6th 2010, 07:05 AM
  5. Smooth function
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 6th 2008, 02:40 PM

Search Tags


/mathhelpforum @mathhelpforum