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Math Help - complex inner product space

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    complex inner product space

    Let C[0,2pi] be the inner product space of complex continuous functions on [0,2pi].

    let { v_k:k=1,2,3,....} be an orthonormal sequence in C[0,2pi], given by v_k(x)=sinkx/pi.

    Give an example of a function u such u\neq\sum_{k=1}<u,v_k>v_k sum from k=1 to infinity.

    thanks for any help.
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    Quote Originally Posted by charikaar View Post
    Let C[0,2pi] be the inner product space of complex continuous functions on [0,2pi].

    let { v_k:k=1,2,3,....} be an orthonormal sequence in C[0,2pi], given by v_k(x)=sinkx/pi.

    Give an example of a function u such u\neq\sum_{k=1}<u,v_k>v_k sum from k=1 to infinity.
    You could try the constant function 1, or a function of the form \cos nx.
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