Vector Space C[-Pi, Pi]

The vector space C[-Pi,Pi] of continuous functions on the interval -Pi to Pi can be made into an inner product space by giving it the following inner product :

In[1]:=

  
  innerproduct[f_,g_,x_]:=Integrate[f g ,{x,-Pi,Pi}]

The norm from this inner product is therefore :

In[2]:=

  
  norm[f_]:=Sqrt[innerproduct[f,f,x]]

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