# Thread: complex inner product space

1. ## 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 $u\neq\sum_{k=1}v_k$ sum from k=1 to infinity.

thanks for any help.

2. Originally Posted by charikaar
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 $u\neq\sum_{k=1}v_k$ sum from k=1 to infinity.
You could try the constant function 1, or a function of the form $\cos nx$.