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Math Help - find a prescription for D^2f+n^2f

  1. #1
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    find a prescription for D^2f+n^2f

    I would like to have some help with the bolded part:

    Let n be a positive integer and let En be the set of mappings f:R->R
    that are given by a prescription of the form

    f(x)=a0 from k=1 to n (akcos(kx)+bksin(kx))

    where ak, bk∈R for each k.
    Prove that Ek is a subspace of Map(R,R).
    If f∈En is the zero mapping, prove that all the coefficients ak, bk must be 0.
    [Hint. Proceed by induction. For this, find a prescription for D2f+n2f.]
    Deduce that the 2n+1 functions
    x->1, x->cos(kx), x->sin(kx) (k=1,...,n)
    form a basis for En.

    Thanks in advance for any help you are able to provide.
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  2. #2
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    Re: find a prescription for D^2f+n^2f

    How am I suppose to regard this D?
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