Thread: Fourier series (pointwise convergence)

I have 3 functions on [-pi,pi[ and i need to describe why the fourier series converges pointwise on [-pi,pi], determine its sumfunction on [-pi,pi] and find out if it's also converges uniformly on [-pi,pi]

the functions are as follows:

1) f(x)= 1 for x in [pi/2,pi[ and 0 for x in [-pi,pi/2[


2) g(x)= |x-pi/2|+|x+pi/2|

3) h(x)= |x+pi/2|

Honestly im a bit lost

Anyway i think they're all piecewise differential c1 functions, and 1) at least is discontinious in -pi and pi.

Originally Posted by Zaph

I have 3 functions on [-pi,pi[ and i need to describe why the fourier series converges pointwise on [-pi,pi], determine its sumfunction on [-pi,pi] and find out if it's also converges uniformly on [-pi,pi]

the functions are as follows:

1) f(x)= 1 for x in [pi/2,pi[ and 0 for x in [-pi,pi/2[


2) g(x)= |x-pi/2|+|x+pi/2|

3) h(x)= |x+pi/2|

Honestly im a bit lost

Anyway i think they're all piecewise differential c1 functions, and 1) at least is discontinious in -pi and pi.

1) At a jump discontinuity what does the Fourier series converge to?

I think you are supposed to look up in your notes or the text book the convergence properties of Fourier series.

CB

Aye you're most likely right, I'll try look some more into it, but i seem to be doing something wrong.

I guess i need to check if the function is piecewise differentiable, cause if it is and has a period of 2pi then it should converge pointwise?

Thanks