- #1

lakmus

- 23

- 1

I try to prove, that function

[itex]f_n = \frac{\sin{nx}}{\pi x}[/itex] converges to dirac delta distribution (in the meaning of distributions sure). On our course we postulated lemma, that guarantee us this if [itex] f_n [/itex]

satisfy some conditions. So I need to show, that [itex]\lim_{n\rightarrow \infty}\int_{a}^{b}f_n \mathrm{d}x[/itex] is

[itex]0[/itex] when [itex]0 [/itex] isn't in [itex] [a,b][/itex] and

[itex]1[/itex] for [itex]0 [/itex] in [itex](a,b)[/itex] .

I never met with problem before, the integral isn't "clasical" function and I don't have clue, how could I even start. I tried do some limit proceses, but it didn't show any concrete value - just estimation . . . (for other function which I found on wiki was possible count the integral and the limit is after easy . . .)

Thaks for any help.