Hilbert Space Help!

  • #1
gravenewworld
1,127
26
How can I show that the space of all continuously differentiable functions on [a,b] denoted W[a,b] with inner product (f,g)=Integral from a to b of (f(x)*conjugate of g(x)+f'(x)*conjugate of g'(x)).

Should I show that the norm does not satisfy the parallelogram law?
 

Answers and Replies

  • #2
Gokul43201
Staff Emeritus
Science Advisor
Gold Member
7,176
22
What do you want to show ?

And just to clarify, you have the inner product defined as :

[tex] \langle f,g \rangle = \int _a ^b (fg^* + f'g'^*)dx [/tex] ?
 
  • #3
gravenewworld
1,127
26
I think I need to show that W[a,b] is not a complete metric space?

And yes that is right inner product.
 

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