Let c > 0 be a constant. For F E Cp (-C, C), the Bessel inequality is

Question

ao squared/ 2 + N E n = 1 (an squared + bn squared) is less than or equal to 1/C { c on top, c on bottom [ f (x)] squared of x, N = 1, 2, ...

Where an and bn are the Fourier coefficients for f (x), -c < x < c.

Using this inequality show that lim an = 0, n ---> infinity and lim bn = 0, n ----> infinity.