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:(adsbygoogle = window.adsbygoogle || []).push({});

"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]

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# Fourier analysis prob

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