proving a certain inequality

Bart · science forum beginner Joined: 07 Jul 2005 Posts: 39

Suppose w(y) is a certain weightfunction, I is the imaginary
unit and D^k(w(y)) is the k'th derivative of w(y), then I'm trying to
prove the following inequality:

abs( int_{0}^{1} w(y)*exp(2*Pi*I*N*y(theta-l))dy )
<= 1/(abs(2*Pi*N*(theta-l)))*int_{0}^{1} abs(D^k(w(y)))dy
for theta not equal l

Now using repeated partial integration, I can get to

abs( int_{0}^{1} w(y)*exp(2*Pi*I*N*y(theta-l))dy )
= ... repeated partial integration ...
= 1/(abs(2*Pi*N*(theta-l)))^k * abs( int_{0}^{1} D^k(w(y))*exp(2*Pi*I*N*(theta-l))dy )

but then I'm stuck because I can't get rid of the exp(2*Pi*I*N*(theta-l))
factor by which D^k(w(y)) is multiplied.

Thanks for your help,
Bart

--

Google