Statement :- We assume the orthagonal sequence
in Hilbert space, now
, the Fourier coefficients are given by:
Then Bessel's inequality give us:
Proof :- We assume the following equation is true
So that,
is projection of
onto the surface by the first
of the
. For any event,
Now, by Pythagoras theorem:
Now, we can deduce that from the above equation that;
For
, we have
Hence, Proved