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Topic: analysis question on periodic functions
Replies: 7   Last Post: Aug 19, 2013 2:25 PM

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Posts: 12,067
Registered: 7/15/05
Re: analysis question on periodic functions
Posted: Aug 19, 2013 2:25 PM
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quasi wrote:
>Followup question:
>Does there exist an element a in R and a function f:R -> R,
>where f is odd, continuous, and periodic with period 1, such
>that, letting S_k = f(a) + f(2*a) + ... + f(k*a), the sequence
>S_1,S_2,S_3, ... is unbounded?


(1) Yes.

(2) No if f is continuously differentiable.


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