Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Proof of inner product for function space

  1. Aug 29, 2009 #1

    SFB

    User Avatar

    Hi I am kinda new to this topic two . I was wondering how can I prove that the following expressions define scalar product. All I can guess that I need to show that they follow the properties of the scalar product.

    But how? If possible, help me with an example .


    1. (f,g)=[tex]\int f(x)g(x)w(x)dx[/tex] where w(x)>0 where x=[0,1]
    2. (f,g)=[tex]\int f'(x)g'(x)dx[/tex] +f(0)g(0)
     
  2. jcsd
  3. Aug 29, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    If this is homework, you should put it on the homework forums, just start a new thread. But I've already asked you, what part of the conditions for those being an inner product are you having a hard time proving?
     
  4. Aug 30, 2009 #3

    Landau

    User Avatar
    Science Advisor

    The only non-trivial part is showing (f,f)=0 --> f=0. You will need continuity of f, so I think you forgot to give information about your function space (probably the space consisting of continous functions f:[0,1]->R).
     
  5. Aug 31, 2009 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Show that each of those satisfies all of the conditions for an inner product. What are those conditions- that is, what is the definition of "inner product"?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Proof of inner product for function space
  1. Inner Product Spaces (Replies: 2)

  2. Inner Product Spaces (Replies: 1)

Loading...