Any idea on how to prove that this is basis for fourier series using Stone-Weierstrass Theorem?
{sin(pi*n*x)/L} from n=1 to n=infinity
with the limits (0,L)
prove:
1=a0*f0 +a1*f1 + a2*f2 + ...... + an*fn (where, an = constants, fn =sin(pi*n*x)/L)
and
sin(pi*n*x)/L * sin(pi*n*x)/L = b0*f0 +b0*f1 + .....bn*fn (where, bn=constants, fn=sin(pi*n*x)/L)
:shock:
{sin(pi*n*x)/L} from n=1 to n=infinity
with the limits (0,L)
prove:
1=a0*f0 +a1*f1 + a2*f2 + ...... + an*fn (where, an = constants, fn =sin(pi*n*x)/L)
and
sin(pi*n*x)/L * sin(pi*n*x)/L = b0*f0 +b0*f1 + .....bn*fn (where, bn=constants, fn=sin(pi*n*x)/L)
:shock: