# Inequality proof

1. Jul 22, 2005

### Townsend

Show that for each complex sequence $$c_1, c_2, ..., c_n$$ and for each integer $$1 \leq H < N$$ one has the inequality

$$| \sum_{n=1}^N c_n|^2 \leq \frac{4N}{H+1} ( \sum_{n=1}^N |c_n|^2 + \sum_{h=1}^H | \rho_N(h)|)$$

Any one.....matt grime perhaps?

note: if anyone actually wants to work this out let me know and I will fill in the missing parts...but don't ask me to do it.... :tongue2:

Last edited: Jul 22, 2005
2. Jul 22, 2005

### honestrosewater

Yeah, that's good. The more fancy meaningless symbols, the better.

3. Jul 22, 2005

### Townsend

There is an important part missing but it is a true bound...not just meaningless...

4. Jul 22, 2005

### honestrosewater

Okay, I'll take your word for it. It would be nice if someone were around to explain it to me.

5. Jul 22, 2005

### Townsend

Yeah...it would take a really smart....creative....mathematician to do so...who would be able to do that I wonder??????

6. Jul 22, 2005

### honestrosewater

... and patient. I've never even worked with complex numbers before. You can just treat them as ordered pairs of real numbers, right? I think I'd like that approach.

7. Jul 22, 2005

### Johnny5

I know the solution, but I won't say to give other people a chance. It's not that hard.

8. Jul 22, 2005

### wolram

Its packman eating flies, so the ansewer must be MxBxHs