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Fourier analysis prob

  1. Oct 10, 2005 #1

    quasar987

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    This seemingly not-so-harsh math problem has me stumped. I tried solving it every free minute I had this weekend but no trails or any combination of them led me anywhere happy. The little ba$tard goes as follow:

    "Consider [itex]f: [-\pi,\pi)\rightarrow \mathbb{R}[/itex] a function (n-1) times continuously differentiable such that [itex]f^{(n-1)}(x)[/itex] is differentiable and continuous except maybe at a finite number of points. If [itex]|f^{(n)}(x)|\leq M[/itex] except maybe at the points of discontinuity, show that the coefficients of the developement of f in a complex fourier serie satisfy

    [tex]|c_r|\leq M/r^n, \ \forall r \neq 0[/itex]

    Edit: [itex]|f^{(n-1)}(x)|\leq M[/itex] --> [itex]|f^{(n)}(x)|\leq M[/itex]
     
    Last edited: Oct 10, 2005
  2. jcsd
  3. Oct 11, 2005 #2

    CarlB

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    Well, with that factor of [itex]r^n[/itex] it sure smells like an integration by parts is involved.

    Carl
     
  4. Oct 11, 2005 #3

    quasar987

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    Thanks for the reply CarlB, I didn't see it that way. I'll try to see what I can do with integration by parts...
     
  5. Oct 11, 2005 #4

    quasar987

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    Integration by parts it was! :biggrin:

    Whenever you need a hug CarlB, I,m here for you.
     
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