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Space of continous functions

  1. Oct 25, 2013 #1
    Is the space of continous functions with the innerproduct being the usual product an inner product space? And if so, why is it we always want to use the space of functions with the norm defined by an integral and not just a simple product? Is it because this IP gives us no notion of orthogonality?
     
  2. jcsd
  3. Oct 25, 2013 #2

    pwsnafu

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    Inner products are scalar valued. Pointwise multiplication results in another function.

    Consider ℝ3 and think about why the dot product has a summation.
     
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