Use Parsevals' Identity.
Parseval's identity - Wikipedia, the free encyclopedia
we know that the sum
Is finite.
Since the series converges we know that the limit
Dear Colleagues,
Could you please help me in solving the following problem:
Show that an element of an inner product space cannot have "too many" Fourier coefficients which are "big"; here, is a given orthonormal sequence; more precisely, show that the number of such that must satisfy .
In fact the most important part -in my opinion- is how we can show that is finite?
Best Regards.
Use Parsevals' Identity.
Parseval's identity - Wikipedia, the free encyclopedia
we know that the sum
Is finite.
Since the series converges we know that the limit
Sorry You need Bessel's inequality then
Bessel's inequality - Wikipedia, the free encyclopedia