Hilbert schmidt norm

1. Dec 3, 2008

dirk_mec1

1. The problem statement, all variables and given/known data

http://img523.imageshack.us/img523/4456/56166304yr3.png [Broken]

2. Relevant equations
http://img356.imageshack.us/img356/2793/40249940is8.png [Broken]

3. The attempt at a solution
I defined K:[a,b] --> [a,b] with $$k(s,t) = \frac{(t-s)^{n-1}}{(n-1)!}$$

I found for the norm:

$$\int_a^b \int_a^b \frac{(t-s)^{2n-2}}{(n-1)!^2}\ \mbox{d}s\ \mbox{d}t =0$$

Is this correct?

Last edited by a moderator: May 3, 2017
2. Dec 3, 2008

morphism

If the norm of blah is zero, then blah is zero. Is blah zero in this case?

3. Dec 4, 2008

dirk_mec1

You're right something is wrong.

But is the integral set up with the correct boundaries?

4. Dec 5, 2008

dirk_mec1

Ok presuming the boundaries are ok I end up with:

$$||A||_{HS} = \frac{2 (b-a)^n}{((n-1)!)^2 (2n-1)(2n)}$$

Is this correct?

5. Dec 5, 2008

morphism

Did you remember to take the square root?

Last edited: Dec 5, 2008
6. Dec 5, 2008

Pere Callahan

You might want to include some characteristic function like $\chi_{\{s\leq t\}}$ in your kernel function.