Results 1 to 3 of 3

Math Help - finding a continues series for convergence in L2

  1. #1
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    finding a continues series for convergence in L2

    i have a function
    f(x)=
    1 for x>0
    0 for x=0

    -1 for x<0


    i need to find a series which belongs to C[T] for which fn(x) converges to f(x) in L2 norm


    in other words

    ||fn(x)-f||_{L_2(T)} ->0 then n->infinity


    how i tried:


    i have dissamble the norm into the integral definition of L2(T)
    so the integral is from -pi to +pi
    and inside we have |fn-f|^2


    then i splited the integral into to parts ,because f=1 for x>0 and f=-1 for x<0.


    i tried to draw a formula that will make 1/n type in the end but
    the continuety doesnt allow
    Last edited by transgalactic; April 9th 2012 at 01:05 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,415
    Thanks
    1853

    re: finding a continues series for convergence in L2

    Your function is not defined for x in [-1, 0) or (0,1]?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Nov 2008
    Posts
    1,401

    re: finding a continues series for convergence in L2

    ohhhh sorry
    i ment
    f(x)=
    1 x>0
    0 x=0
    -1 x<0
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Finding radius of convergence on a series
    Posted in the Calculus Forum
    Replies: 5
    Last Post: September 1st 2011, 08:11 AM
  2. Replies: 1
    Last Post: February 22nd 2011, 07:47 AM
  3. Finding the convergence of the infinite series
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 7th 2009, 06:25 PM
  4. Finding convergence of a series???
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 27th 2009, 04:22 AM
  5. Replies: 5
    Last Post: May 10th 2009, 07:25 PM

Search Tags


/mathhelpforum @mathhelpforum