Inner product of functions

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  • #1
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Main Question or Discussion Point

What is the proof that the inner product of two functions f(x) and g(x) is

[tex]
\int_{a}^{b} f(x)g(x)dx
[/tex]

Or is this actually a definition of the inner product for functions? If it is a definition, then what is it based on?

Thank you
 
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Answers and Replies

  • #2
arildno
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You've gotten it backwards:
That particular integral can be shown to fulfill the PROPERTIES OF AN INNER PRODUCT.

For your info, if w(x) is a positive integrable function, the following can also be shown to be an inner product:
[tex]<f,g>\mid_{w}=\int_{a}^{b}f(x)g(x)w(x)dx[/tex]
 
  • #3
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