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C^1 functions

  1. Jan 28, 2009 #1
    Im having trouble showing that given a sequence of uniformly bounded C^1([a,b],R) functions,
    the derivative sequence is uniformly bounded.
    Any suggestions are helpfull
     
  2. jcsd
  3. Jan 28, 2009 #2

    Dick

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    If by 'uniformly bounded', you mean |f_n(x)|<M for some constant M, it's not true that the derivatives are necessarily bounded.
     
  4. Jan 28, 2009 #3
    Youre right, the reason I ask is b/c Im trying to prove that every bounded sequence in C^1 has a convergent subsequence, Arzela Ascoli type problem.
     
  5. Jan 28, 2009 #4

    Dick

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    What do you mean by a 'bounded sequence' in C^1? sin(n*x) is a bounded sequence in C^1 (in the sense |f_n|<=1). But it has no convergent subsequence. You need some sort of premise to get the equicontinuity from.
     
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